Function notation — ISEE Upper practice questions

70 practice questions in the app
Free

Practice 70 Function notation questions in the app

What this topic is

Function notation uses f(x) as a name for an output, not as f times x.

Evaluating f at five means replacing every x in the rule with five. Composite expressions such as g(f(x)) are worked from the inside out: find f of the input first, then feed that result into g; reversing the order is a classic error, and its result usually appears among the choices.

Some questions restrict x to an interval and ask for a maximum, which requires checking the endpoints and any turning point rather than plugging in only the largest x.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

What is the maximum value of $y$ if $y = 2 x^{2} - 3$ for $- 1 \leq x \leq 2$ ?

- 3

✗ Not this one

- 1

✗ Not this one5✓ Correct8✗ Not this one

Show answer

Answer: C — 5

Since $x^{2}$ is largest at $x = 2$ on this interval, the maximum is $2 (2)^{2} - 3 = 8 - 3 = 5$ .

Question 2Easier

If $f (x) = x^{2} - 3$ , what is the value of $f (4)$ ?

5✗ Not this one11✗ Not this one13✓ Correct29✗ Not this one

Show answer

Answer: C — 13

Substitute 4 for $x$ : $f (4) = 4^{2} - 3 = 16 - 3 = 13$ .

Question 3Easier

If $f (x) = x + 4$ and $g (x) = x^{2}$ , what is $g (f (- 1))$ ?

1✗ Not this one5✗ Not this one9✓ Correct25✗ Not this one

Show answer

Answer: C — 9

Evaluate the inner function first: $f (- 1) = - 1 + 4 = 3$ . Then $g (f (- 1)) = g (3) = 3^{2} = 9$ .

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 70 Function notation questions in the app

Function notation — ISEE Upper practice questions

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning