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PSAT Math Question of the Day

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Thursday, September 17, 2026

The graph of a linear function $g$ is shown in the $xy$ -plane. The function $h$ is defined by $h(x)=g(x-3)+4$ . What is the $x$ -intercept of the graph of $h$ ?

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Question of the Day

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The graph of a linear function $g$ is shown in the $xy$ -plane. The function $h$ is defined by $h(x)=g(x-3)+4$ . What is the $x$ -intercept of the graph of $h$ ?

$(5,0)$ (correct answer)
$(-1,0)$
$(7,0)$
$(1,0)$

Explanation: From the graph, line $g$ passes through $(0,-8)$ and $(4,0)$ , so it has slope $\frac{0-(-8)}{4-0}=2$ and equation $g(x)=2x-8$ . The transformed function is $h(x)=g(x-3)+4=2(x-3)-8+4=2x-6-8+4=2x-10$ . To find the $x$ -intercept, set $h(x)=0$ : $2x-10=0$ , so $x=5$ . The $x$ -intercept is $(5,0)$ .