Chapter 11 Test

1) Does a function exist for which the input value is a state and the output value is the state’s capital city?

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2) Use the vertical line test to determine whether the graph represents a function.

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Evaluate the given function.

3) $f\left(x\right)=-2x+35,f\left(-8\right)$ 

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4) $f\left(x\right)=5x+16,f\left(6a-5\right)$ 

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5) $f\left(x\right)=x^2-15x+54,f\left(-9\right)$ 

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6) Determine the domain and range of the function $f\left(x\right)$ that has been graphed.

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Graph the function.

7) $f\left(x\right)=-4x+6$ 

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8) $f\left(x\right)=\frac{2}{3}x-4$ 

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9) A ceramics shop holds birthday parties for children. They charge a party fee in addition to a fee for each guest attending. A party with 10 guests costs $105, whereas a party with 25 guests costs $210. Find a linear function $f\left(x\right)=mx+b$ whose input is the number of guests and whose output is the cost of the party.

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Graph the function by shifting. Label the vertex, y-intercept, and any x-intercepts. Round to the nearest tenth if necessary.

10) $f\left(x\right)={\left(x+4\right)}^2-6$ 

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11) $f\left(x\right)=-{\left(x+3\right)}^2+4$ 

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12) A young child throws a ball upward with an initial velocity of 20 feet/second. The height of the ball (in feet) after t seconds is given by the function $h\left(t\right)=-16t^2+20t+3$. What is the maximum height the ball reaches?

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Graph the given function and state its domain and range.

13) $f\left(x\right)=\left|x+4\right|-5$ 

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14) $f\left(x\right)=\sqrt{x+1}-3$ 

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15) $f\left(x\right)={\left(x+1\right)}^3+8$ 

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16) Determine the function $f\left(x\right)$  on the graph.

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17) If $f\left(x\right)=5x-2$  and $g\left(x\right)=x^2-4x-13,$ find $\left(f+g\right)\left(-2\right)$.

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18) If $f\left(x\right)=x-6$  and $g\left(x\right)=x^2+6x+36,$ find $\left(f\cdot g\right)\left(x\right)$.

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Let $f\left(x\right)=x+7$ and $g\left(x\right)=2x-8$. Find the following.

19) $\left(f\circ g\right)\left(6\right)$ 

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20) $\left(g\circ f\right)\left(6\right)$ 

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For the given functions $f\left(x\right)$ and $g\left(x\right)$, find $\left(f\circ g\right)\left(x\right)$.

21) $f\left(x\right)=4x+13,g\left(x\right)=-2x+23$ 

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22) $f\left(x\right)=x^2-9x-30,g\left(x\right)=x+12$ 

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23) Use the horizontal-line test to determine whether the function is one-to-one.

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24) Determine whether $f\left(x\right)=2x-16$ and $g\left(x\right)=\frac{1}{2}x+8$ are inverse functions. Recall that $f\left(x\right)$ and $g\left(x\right)$ are inverse functions if $\left(f\circ g\right)\left(x\right)=x$ and $\left(g\circ f\right)\left(x\right)=x$.

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For the given function $f\left(x\right)$, find $f^{-1}\left(x\right)$.

25) $f\left(x\right)=-4x+20$ 

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26) $f\left(x\right)=\frac{x-9}{4x}$ 

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