Functions, transformations, composition and inverses

Reading a function

Question 1

A function is $x^2$ when $x < 2$ and $3x - 1$ when $x \ge 2$ . What is $f(2)$ ?

A.Both 4 and 5B.4C.5D.Undefined, because 2 is on the boundary

Question 2

Which interval is the same as $-4 \le x < 1$ ?

A.

[-4, 1)

B.

(-4, 1)

C.

(-4, 1]

D.

[-4, 1]

Question 3

What is the domain of $f(x) = \dfrac{x + 2}{x^2 - 9}$ ?

A.Every real number except 9B.Every real number except 3 and -3C.Every real numberD.Every real number except -2

Question 4

For $f(x) = x^2 - 3x$ , what is $f(-2)$ ?

A.-10B.2C.10D.-2

Question 5

What is the average rate of change of $f(x) = x^2 + 1$ from $x = -1$ to $x = 3$ ?

A.1B.4C.2D.8

Question 6

With $f(x) = x^2 + 1$ and $g(x) = x - 4$ , what is $(f \circ g)(x)$ ?

A.

(x^2 + 1)(x - 4)

B.

x^2 - 16 + 1

C.

x^2 - 3

D.

(x - 4)^2 + 1

Question 7

What is the inverse of $f(x) = 2x + 6$ ?

A.

f^{-1}(x) = \dfrac{1}{2x + 6}

B.

f^{-1}(x) = 2x - 6

C.

f^{-1}(x) = \dfrac{x - 6}{2}

D.

f^{-1}(x) = \dfrac{x + 6}{2}

Question 8

How does the graph of $y = f(x - 3) + 2$ compare with the graph of $y = f(x)$ ?

A.Moved 3 right and 2 upB.Moved 3 right and 2 downC.Moved 3 left and 2 upD.Moved 2 right and 3 up

Question 9

Which of these needs its domain restricted before it has an inverse function?

A.

f(x) = 5x - 2

B.

f(x) = x - 7

C.

f(x) = x^3

D.

f(x) = x^2 + 1

9 questions left to answer.