The function h is increasing for all values of x, and the graph of h is concave up for all values of x. Let the function k be the inverse of h. Which of the following statements about k is true?

k is increasing, and the graph of k is concave down.

k is increasing, and the graph of k is concave up.

k is decreasing, and the graph of k is concave up.

k is decreasing, and the graph of k is concave down.

The function g is given by $$g\left(x\right)=\log_3\left(x-4\right)$$ . Which of the following statements about the construction of the inverse of g is true?

The inverse of g can be constructed, and the graph of $$g^{-1}$$ has domain of all real values of x.

The inverse of g cannot be constructed because the graph of g is not defined for all real values of x.

The inverse of g can be constructed, and the graph of $$g^{-1}$$ has domain x > 4.

The inverse of g can be constructed, and the graph of $$g^{-1}$$ has range of real values of y.

The function is given by $$g\left(x\right)=\log_4x$$ Which of the following statements about the inverse of g is true?

The inverse of g is given by $$g^{-1}\left(x\right)=4^x$$ and is defined for all real values of x.

The inverse of g is given by $$g^{-1}\left(x\right)=x^4$$ and is defined for all real values of x.

The inverse of g is given by $$g^{-1}\left(x\right)=4^x$$ and is defined only for x > 4.

g does not have an inverse because the graph of g is undefined for x $$\le$$ 0.

The points (-3 , 1/8) and (4 , 16) are on the graph of the exponential function h given by $$h\left(x\right)=\ b^x$$ where b > 1. Which of the following statements about the graph of $$k\left(x\right)=\log_bx$$ is true?

The points (1/8, -3) and (16, 4) are both on the graph of h because $$k=h^{-1}$$

The points (-3, 1/8) and (4, 16) are both on the graph of h because $$k=h^{-1}$$ .

The points (1/3, 1/8) and (4, 16) are both on the graph of h because $$k=h^{-1}$$

The point (16, 4) is on the graph of h but the point (1/8, -3) is not on the graph of h because the domain of h is restricted to x > 0, thus the range of k is restricted to y > 0.

Which of the following claim and explanation statements best fits these data?

f is best modeled by a logarithmic function, because the input values change proportionately as output values increase in equal-length intervals.

f is best modeled by an exponential function, because the input values change proportionately as output values increase in equal-length intervals.

f is best modeled by an exponential function, because the output values change proportionately as input values increase in equal-length intervals.

f is best modeled by a logarithmic function, because the output values change proportionately as input values increase in equal-length intervals.

The table shows values for a function h at selected values of X. Which of the following claim and explanation statements best fits these data?

h is best modeled by a logarithmic function, because the input values change proportionately as output values increase in equal-length intervals.

h is best modeled by an exponential function, because the input values change proportionately as output values increase in equal-length intervals.

h is best modeled by an exponential function, because the output values change proportionately as input values increase in equal-length intervals.

h is best modeled by a logarithmic function, because the output values change proportionately as input values increase in equal-length intervals.

The table shows values for a function k at selected values of X. Which of the following claim and explanation statements best fits these data?

k is best modeled by an exponential function, because the output values change proportionately as input values increase in equal-length intervals.

k is best modeled by an exponential function, because the input values change proportionately as output values increase in equal-length intervals.

k is best modeled by a logarithmic function, because the input values change proportionately as output values increase in equal-length intervals.

k is best modeled by a logarithmic function, because the output values change proportionately as input values increase in equal-length intervals.

Let f be the logarithmic function given by $$f\left(x\right)=3\log_{10}x$$ . Which of the following statements about f is true?

f is increasing, and the graph of f is concave down.

f is increasing, and the graph of f is concave up.

f is decreasing, and the graph of f is concave up.

f is decreasing, and the graph of f is concave down.

Let g be the logarithmic function given by $$g\left(x\right)=-2\log_3x$$ . Which of the following statements about g is true?

g is decreasing, and the graph of g is concave up.

g is increasing, and the graph of g is concave up.

g is increasing, and the graph of g is concave down.

g is decreasing, and the graph of g is concave down.

Let h be the logarithmic function given by $$h\left(x\right)=3-2\log_6x$$ . Which of the following statements about h is true?

h is decreasing, and the graph of h is concave up.

h is increasing, and the graph of h is concave up.

h is increasing, and the graph of h is concave down.

h is decreasing, and the graph of h is concave down.

Let f be the logarithmic function given by $$f\left(x\right)=5-4\log_7x$$ . Which of the following statements about the end behavior of f is true?

As the input values of f decrease arbitrarily close to 0, the output values increase without bound.

As the input values of f increase without bound, the output values increase without bound.

As the input values of f increase without bound, the output values get arbitrarily close to 0.

As the input values of f decrease arbitrarily close to 0, the output values decrease without bound.

Let g be the logarithmic function given by $$g\left(x\right)=3\log_2x$$ . Which of the following statements about the end behavior of g is true?

As the input values of g decrease arbitrarily close to 0, the output values decrease without bound.

As the input values of g increase without bound, the output values decrease without bound.

As the input values of g increase without bound, the output values get arbitrarily close to 0.

As the input values of g decrease arbitrarily close to 0, the output values increase without bound.

Let $$f\left(x\right)=\log_2x$$ and let $$g\left(x\right)=\log_2\left(6x\right)$$ . Which of the following statements about the graphs of f and g is true?

The graph of g is a vertical translation of the graph of f by $$\log_26$$ units.

The graph of g is a horizontal translation of the graph f of by $$-\log_26$$ units.

The graph of g is a horizontal dilation of the graph of f by a factor of 6.

The graph of g is a vertical dilation of the graph of f by a factor of 6.

Let $$h\left(x\right)\ =\ln\ x$$ and let $$k\left(x\right)=\ln\left(\frac{x}{2}\right)$$ . Which of the following statements about the graphs of h and k is correct?

The graph of h is a horizontal dilation of the graph of k by a factor of 1/2.

The graph of k is a horizontal dilation of the graph of h by a factor of 1/2 .

The graph of k is a vertical translation of the graph of h by -2 units.

The graph of h is a vertical translation of the graph of k by -2 units.

What are all values of x for which $$\log_2x^2-\log_24=3$$ ?

$$x=4\sqrt[]{2}$$ and $$x=-4\sqrt[]{2}$$

$$x=\sqrt[]{2}$$ and $$x=-\sqrt[]{2}$$

$$x=\sqrt[]{7}$$ and $$x=-\sqrt[]{7}$$

$$x=2\sqrt[]{3}$$ and $$x=-2\sqrt[]{3}$$

AP Precalculus Unit 2 Part B Passwater's MCQ Exam Review

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[-5, 4]

[-4, 5]

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[-1/4, 5]

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A) 2

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D) 7

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