APPC 2.9-2.13 MCQ Test Review

Categorize

Options (4)

Match the table to the correct function type.

Logarithmic

Exponential

Linear

Quadratic

Multiple Choice

The table gives values of a function h for selected values of x. Which of the following statements with reasons is correct?

• The function h represents exponential growth because as input values change additively, output values change multiplicatively.

• The function h represents exponential growth because as input values change multiplicatively., output values change additively,

• The function h represents logarithmic growth because as input values change additively, output values change multiplicatively.

• The function h represents logarithmic growth because as input values change multiplicatively, output values change additively.

Multiple Choice

The function f is an increasing function such that every time the input values multiply by 3, the corresponding output values increase by 1. Which of the following could define f(x)?

• $$3^x$$

• $$\left(\frac{1}{3}\right)^x$$

• $$\log_3\left(x\right)$$

• $$\sqrt[3]{x}$$

Multiple Choice

The table gives values of a function g for selected values of x. Which of the following is a verbal representation of $$g^{-1}\left(x\right)$$ , the inverse function of g?

• $$g^{-1}\left(x\right)$$ is logarithmic with the input values increasing by 1 every time output values quadruple.

• $$g^{-1}\left(x\right)$$ is logarithmic with the output values increasing by 1 every time input values quadruple.

• $$g^{-1}\left(x\right)$$ is exponential with the input values increasing by 1 every time output values quadruple.

• $$g^{-1}\left(x\right)$$ is exponential with the output values increasing by 1 every time input values quadruple

Multiple Choice

Which of the following could NOT be the end behavior of a logarithmic function?

• $$\lim_{x\rightarrow0^+}f\left(x\right)=\infty$$ $$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$$

• $$\lim_{x\rightarrow0^+}f\left(x\right)=-\infty$$ $$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$$

• $$\lim_{x\rightarrow\infty}f\left(x\right)=\infty$$ $$\lim_{x\rightarrow0^+}f\left(x\right)=-\infty$$

• $$\lim_{x\rightarrow\infty}f\left(x\right)=-\infty$$ $$\lim_{x\rightarrow0^+}f\left(x\right)=-\infty$$

Match

Match the following

• $$f\left(x\right)=3^x$$

• $$g\left(x\right)=2\log_3x$$

• $$h\left(x\right)=-3\ln$$

• $$n\left(x\right)=-\left(2\right)^x$$

Increases at an increasing rate

Increases at a decreasing rate

Decreases at an increasing rate

Decreases at a decreasing rate

• Increases at an increasing rate

• Increases at a decreasing rate

• Decreases at an increasing rate

• Decreases at a decreasing rate

Match

Match the following

• $$g\left(x\right)=2^x$$

• $$h\left(x\right)=\ln x$$

• $$n\left(x\right)=-2\ \log x$$

• $$f\left(x\right)=-3\left(2\right)^x$$

Increasing and concave up

Increasing and concave down

Decreasing and concave up

Decreasing and concave down

• Increasing and concave up

• Increasing and concave down

• Decreasing and concave up

• Decreasing and concave down

Multiple Choice

The graph of a logarithmic function f is given. For the function g (not shown), it is known that f(g(x))=x for all values of x. Which is true about g and the graph of y=g(x)?

• 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 up

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

Multiple Choice

The exponential function $$g$$ is given by $$g\left(x\right)=2^x$$ . Which of the following expressions defines $$g^{-1}\left(x\right)$$ ?

• $$\sqrt[2]{x}$$

• $$\sqrt[x]{2}$$

• $$\log_x2$$

• $$\log_2x$$

Multiple Choice

If $$4^m=64$$ , which of the following is also true?

• $$m=\log_464$$

• $$64=\log_4m$$

• $$\sqrt[m]{4}=64$$

• $$64=m^4$$