Function notation — ISEE Upper practice questions

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.

Section: Quantitative Reasoning 37 questions on the paper
70 practice questions in the app

Sample questions

Question 1

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

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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 2

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

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Answer: C — 13

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

Question 3

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

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Answer: C — 9

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

Practice 70 Function notation questions in the app

Function notation — ISEE Upper practice questions

Sample questions

More ISEE Upper topics

Quantitative Reasoning