Function notation — ISEE Upper practice questions

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Practice 70 Function notation questions in the app

What this topic is

Function notation on the ISEE Upper Quantitative Reasoning section covers reading f(x) and related symbols, substituting a number for the input, and combining two functions.

A student has to evaluate a linear or quadratic rule at a stated value, compute a composition such as g of f of a number, and sometimes find a maximum of y on a closed interval. Questions are multiple-choice, and the choices are usually small integers.

Common traps include reversing composition order, treating the function as multiplication rather than substitution, and reporting a vertex that lies outside the given domain instead of checking the endpoints.

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 $y=2x^2-3$ for $-1\le x\le 2$ ?

-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