ACT · Mathematics

Functions

24 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 24 questions

If $f (x) = 4 x^{2} + 2$ , what is $f (2)$ ?
If $f (x) = x^{2} - 5 x + 4$ , what is $f (- 2)$ ?
If $f (x) = 2 x^{2} - 2 x + 3$ , what is $f (4)$ ?
If $f (x) = x^{2} - 4 x + 6$ , what is $f (1)$ ?
If $f (x) = 3 x^{2} - 4 x - 1$ , what is $f (4)$ ?
If $f (x) = 3 x^{2} - x + 4$ , what is $f (- 3)$ ?
If $f (x) = x^{2} - 4 x$ , what is $f (- 2)$ ?
If $f (x) = 2 x^{2} - 5 x - 1$ , what is $f (3)$ ?
If $f (x) = x^{2} + 3 x - 2$ , what is $f (3)$ ?
If $f (x) = 3 x^{2} - x - 6$ , what is $f (2)$ ?
If $f (x) = 3 x^{2} - 3 x + 1$ , what is $f (- 2)$ ?
If $f (x) = 4 x^{2} - 2 x - 1$ , what is $f (- 1)$ ?
If $f (x) = x^{2} - 2 x + 1$ , what is $f (4)$ ?
If $f (x) = 2 x^{2} + 2 x + 6$ , what is $f (4)$ ?
If $f (x) = 3 x^{2} - 3 x$ , what is $f (3)$ ?
If $f (x) = 2 x^{2} + 3 x - 3$ , what is $f (- 3)$ ?
If $f (x) = x^{2} - 4 x + 1$ , what is $f (- 1)$ ?
If $f (x) = x^{2} - 4 x - 2$ , what is $f (1)$ ?
If $h (x) = \frac{3 x - 1}{x + 2}$ for $x \neq = - 2$ , what is $h^{- 1} (5)$ ?
The function $f (x) = a x + b$ has $a > 0$ , and $f (f (x)) = 4 x + 9$ for all $x$ . What is $f (5)$ ?
Let $f (x) = 2 x + 3$ and $g (x) = x^{2} - 1$ . For which values of $x$ does $f (g (x)) = g (f (x))$ ?
If $f (x) = \frac{x + 1}{x - 3}$ for $x \neq = 3$ , what is $f^{- 1} (5)$ ?
The graph of $y = f (x)$ has its lowest point at $(2, - 3)$ . What are the coordinates of the highest point or lowest point of the graph of $y = - 2 f (x + 1) + 4$ ?
Let $f (x) = x^{2} - 4$ for $x < 1$ and $f (x) = 3 x + 2$ for $x \geq 1$ . What is the value of $f (f (- 1)) + f (1)$ ?

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