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The graph of
y=f(x+3) is shown. For which value of
x, rounded to the nearest whole number, must
f(x)=0 ?

The graph of $y=f(x+3)$ is shown. For which value of $x$ , rounded to the nearest whole number, must $f(x)=0$ ?

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Find the length of the transverse or conjugate axes of a hyperbola

Full solution

Q. The graph of

y=f(x+3)

is shown. For which value of

x

, rounded to the nearest whole number, must

f(x)=0

?

Understand Transformation: To solve for the value of $x$ where $f(x) = 0$ , we need to understand the transformation applied to the function $f(x)$ to get the graph of $y = f(x+3)$ . $\newline$ The graph of $y = f(x+3)$ is a horizontal shift of the graph of $y = f(x)$ to the left by $3$ units. $\newline$ This means that the $x$ -values on the graph of $y = f(x+3)$ are $3$ units less than the corresponding $x$ -values on the graph of $y = f(x)$ .
Find value of $x$ for $f(x)=0$ : To find when $f(x)=0$ , we need to find what value of $x$ results in $f(x+3)=0$ . $\newline$ Since $f(x+3)=0$ , it implies that $x+3=0$ , because when you input $x = −3$ , you get $(−3)+3=0$ . $\newline$ Hence, the value of $x$ is $-3$ , when $f(x)=0$ .

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