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Solve the problem. -A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4−km4 - \mathrm { km } by 6-km rectangle. As the camera zooms out, the length 1 and width ww of the rectangle increase at a rate of 3 km/sec\mathrm { km } / \mathrm { sec } . How long does it take for the area A to be at least 4 times its original size?


A) 1.61sec1.61 \mathrm { sec }
B) 9.7sec9.7 \mathrm { sec }
C) 4.94sec4.94 \mathrm { sec }
D) 3.28sec3.28 \mathrm { sec }

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A

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - y=(x+17) 2y = ( x + 17 ) ^ { 2 }


A) Shift the graph of y=x2y = x ^ { 2 } down 17 units.
B) Shift the graph of y=x2y = x ^ { 2 } up 17 units.
C) Shift the graph of y=x2y = x ^ { 2 } right 17 units.
D) Shift the graph of y=x2y = x ^ { 2 } left 17 units.

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Determine whether the graph is the graph of a function. -Determine whether the graph is the graph of a function. -

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Perform the requested operation or operations. Find the domain of each. - f(x) =2x+7,g(x) =6x2f ( x ) = 2 x + 7 , g ( x ) = 6 x ^ { 2 } Find (fg) (x) ( \mathrm { fg } ) ( \mathrm { x } ) .


A) 12x3+42x212 x ^ { 3 } + 42 x ^ { 2 } ; domain: (−∞,∞) ( - \infty , \infty )
B) 12x+4212 x + 42 ; domain: (−∞,∞) ( - \infty , \infty )
C) 6x2+2x+76 x ^ { 2 } + 2 x + 7 ; domain: (−∞,∞) ( - \infty , \infty )
D) 12x2+42x12 x ^ { 2 } + 42 x ; domain: (−∞,∞) ( - \infty , \infty )

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Find two functions defined implicitly by the given relation. - 3x2−y2=43 x ^ { 2 } - y ^ { 2 } = 4


A) y=x32y = \frac { x \sqrt { 3 } } { 2 } or y=−x32y = - \frac { x \sqrt { 3 } } { 2 }
B) y=3x−4y = \sqrt { 3 } x - \sqrt { 4 } or y=−3x+4y = - \sqrt { 3 } x + \sqrt { 4 }
C) y=3x2−4y = \sqrt { 3 x ^ { 2 } - 4 } or y=3x2+4y = \sqrt { 3 x ^ { 2 } + 4 }
D) y=3x2−4y = \sqrt { 3 x ^ { 2 } - 4 } or y=−3x2−4y = - \sqrt { 3 x ^ { 2 } - 4 }

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Perform the requested operation or operations. - f(x) =x2+9;g(x) =x−1f ( x ) = x ^ { 2 } + 9 ; g ( x ) = \sqrt { x - 1 } Find g(f(x) ) g ( f ( x ) ) .


A) g(f(x) ) =(x−1) (x2+9) g ( f ( x ) ) = ( \sqrt { x - 1 } ) \left( x ^ { 2 } + 9 \right)
B) g(f(x) ) =x2+8g ( f ( x ) ) = \sqrt { x ^ { 2 } + 8 }
C) g(f(x) ) =x−1x2+9g ( f ( x ) ) = \frac { \sqrt { x - 1 } } { x ^ { 2 } + 9 }
D) g(f(x) ) =x+8g ( f ( x ) ) = x + 8

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Match the numerical model to the corresponding model. - x345678y111417202326\begin{array}{r|rrrrrr}\mathrm{x} & 3 & 4 & 5 & 6 & 7 & 8 \\\hline \mathrm{y} & 11 & 14 & 17 & 20 & 23 & 26\end{array}


A)
Match the numerical model to the corresponding model. - \begin{array}{r|rrrrrr} \mathrm{x} & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \mathrm{y} & 11 & 14 & 17 & 20 & 23 & 26 \end{array} A) B) C) D)
B)
Match the numerical model to the corresponding model. - \begin{array}{r|rrrrrr} \mathrm{x} & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \mathrm{y} & 11 & 14 & 17 & 20 & 23 & 26 \end{array} A) B) C) D)

C)

Match the numerical model to the corresponding model. - \begin{array}{r|rrrrrr} \mathrm{x} & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \mathrm{y} & 11 & 14 & 17 & 20 & 23 & 26 \end{array} A) B) C) D)
D)
Match the numerical model to the corresponding model. - \begin{array}{r|rrrrrr} \mathrm{x} & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \mathrm{y} & 11 & 14 & 17 & 20 & 23 & 26 \end{array} A) B) C) D)

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Find the asymptote(s) of the given function. - f(x) =x−3x2−36f ( x ) = \frac { x - 3 } { x ^ { 2 } - 36 } vertical asymptotes(s)


A) x=−6x = - 6
B) x=3x = 3
C) x=6,x=−6x = 6 , x = - 6
D) x=6x = 6

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C

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the graph of y1 across an axis. - Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the graph of y1 across an axis. - A) f ( x ) = \sqrt { x - 6 } B) f ( x ) = \sqrt { x + 6 } C) f ( x ) = \sqrt { x } + 6 D) f ( x ) = \sqrt { x } - 6


A) f(x) =x−6f ( x ) = \sqrt { x - 6 }
B) f(x) =x+6f ( x ) = \sqrt { x + 6 }
C) f(x) =x+6f ( x ) = \sqrt { x } + 6
D) f(x) =x−6f ( x ) = \sqrt { x } - 6

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Choose the one alternative that best completes the statement or answers the question. -For the graph shown, at which point does the function change from increasing to decreasing? Choose the one alternative that best completes the statement or answers the question. -For the graph shown, at which point does the function change from increasing to decreasing? A) x = 0 B) x = 2 C) x = 2 / 3 D) x = - 1.19


A) x=0x = 0
B) x=2x = 2
C) x=2/3x = 2 / 3
D) x=−1.19x = - 1.19

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Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. - A) Linear regression B) Quadratic regression C) Cubic regression D) Sinusoidal regression E) Exponential regression


A) Linear regression
B) Quadratic regression
C) Cubic regression
D) Sinusoidal regression
E) Exponential regression

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Fill in the blanks to complete the statement. -The graph of y=0.8∣−x∣−10y = 0.8 | - x | - 10 can be obtained from the graph of y=∣x∣y = | x | by reflecting across the Fill in the blanks to complete the statement. -The graph of y = 0.8 | - x | - 10 can be obtained from the graph of y = | x | by reflecting across the -axis, shrinking vertically by a factor of and then shifting vertically units in the ? direction . A) y ; - 0.8 ; 10 ; downward B) x ; 10 ; 0.8 ; upward C) x ; 0.8 ; 10 ; downward D) \mathrm { y } ; 0.8 ; 10 ; downward -axis, shrinking vertically by a factor of 11ecc462_eee5_8183_841e_b1b874fd7cdc_TB8181_00 and then shifting vertically11ecc462_eee5_8183_841e_b1b874fd7cdc_TB8181_00 units in the ? direction 11ecc462_eee5_8183_841e_b1b874fd7cdc_TB8181_00 .


A) y;−0.8;10y ; - 0.8 ; 10 ; downward
B) x;10;0.8x ; 10 ; 0.8 ; upward
C) x;0.8;10x ; 0.8 ; 10 ; downward
D) y;0.8;10\mathrm { y } ; 0.8 ; 10 ; downward

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Perform the requested operation or operations. Find the domain of each. - f(x) =x;g(x) =6x−7f ( x ) = \sqrt { x } ; g ( x ) = 6 x - 7 Find f/gf / g .


A) (f/g) (x) =x6x−7;( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ; domain {x∣x≥0,x≠76}\left\{ x \mid x \geq 0 , x \neq \frac { 7 } { 6 } \right\}
B) (f/g) (x) =6x−7x;( f / g ) ( x ) = \frac { 6 x - 7 } { \sqrt { x } } ; domain {x∣x≥0}\{ x \mid x \geq 0 \}
C) (f/g) (x) =x6x−7( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ; domain {x∣x≠0}\{ x \mid x \neq 0 \}
D) (f/g) (x) =x6x−7;( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ; domain {x∣x≠76}\left\{ x \mid x \neq \frac { 7 } { 6 } \right\}

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Solve the equation algebraically. - x(x−5) =14x ( x - 5 ) = 14


A) −2;7- 2 ; 7
B) 0;50 ; 5
C) 2;−72 ; - 7
D) 5,−145 , - 14

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Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - g(x) =x2−3xxg ( x ) = \frac { x ^ { 2 } - 3 x } { x } Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - g ( x ) = \frac { x ^ { 2 } - 3 x } { x } A) No B) No C) Yes; removable D) No


A)
Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - g ( x ) = \frac { x ^ { 2 } - 3 x } { x } A) No B) No C) Yes; removable D) No

No

B)
Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - g ( x ) = \frac { x ^ { 2 } - 3 x } { x } A) No B) No C) Yes; removable D) No
No
C)
Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - g ( x ) = \frac { x ^ { 2 } - 3 x } { x } A) No B) No C) Yes; removable D) No
Yes; removable
D)
Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - g ( x ) = \frac { x ^ { 2 } - 3 x } { x } A) No B) No C) Yes; removable D) No

No

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C

Find the asymptote(s) of the given function. - f(x) =x−4x2+1f ( x ) = \frac { x - 4 } { x ^ { 2 } + 1 } vertical asymptotes(s)


A) None
B) x=−1x = - 1
C) x=1x = 1
D) x=2,x=−2x = 2 , x = - 2

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Perform the requested operation or operations. - f(x) =1x−6;g(x) =xf ( x ) = \frac { 1 } { x - 6 } ; g ( x ) = \sqrt { x } Find f(g(x) ) f ( g ( x ) ) .


A) f(g(x) ) =(x−6) xf ( g ( x ) ) = ( x - 6 ) \sqrt { x }
B) f(g(x) ) =xx−6f ( g ( x ) ) = \frac { \sqrt { x } } { x - 6 }
C) f(g(x) ) =1x−6f ( g ( x ) ) = \frac { 1 } { \sqrt { x } - 6 }
D) f(g(x) ) =1x−6f ( g ( x ) ) = \sqrt { \frac { 1 } { x - 6 } }

Correct Answer

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Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - f(x) =4xf ( x ) = \frac { 4 } { x } Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - f ( x ) = \frac { 4 } { x } A) Yes; removable B) No C) No D) Yes; non-removable


A)
Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - f ( x ) = \frac { 4 } { x } A) Yes; removable B) No C) No D) Yes; non-removable
Yes; removable

B)
Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - f ( x ) = \frac { 4 } { x } A) Yes; removable B) No C) No D) Yes; non-removable
No
C)
Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - f ( x ) = \frac { 4 } { x } A) Yes; removable B) No C) No D) Yes; non-removable
No

D)
Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - f ( x ) = \frac { 4 } { x } A) Yes; removable B) No C) No D) Yes; non-removable

Yes; non-removable

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Find the asymptote(s) of the given function. - f(x) =x−7x2+6xf ( x ) = \frac { x - 7 } { x ^ { 2 } + 6 x } vertical asymptotes(s)


A) x=6x = 6
B) x=0,x=−6x = 0 , x = - 6
C) x=−6x = - 6
D) x=7x = 7

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Identify which of the twelve basic functions listed below fit the description given. -The one function that is decreasing from (0,∞) ( 0 , \infty )


A) y=1xy = \frac { 1 } { x }
B) y=∣x∣y = | x |
C) y=ln⁡xy = \ln x
D) y=11+e−xy = \frac { 1 } { 1 + e ^ { - x } }

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