Question

let f(x) be the parent function graphed below and let g(x) be f(x) after being reflected about the y - axis. write the equation for g(x). draw show your work here hint: to add an exponent (x^n), type \exponent\ or press \^\. g(x)=

Explanation:

Step1: Recall reflection rule

When a function $y = f(x)$ is reflected about the $y$-axis, the transformation rule is $g(x)=f(-x)$.

Step2: Determine the parent - function

The parent - function $f(x)$ appears to be $f(x)=x^{2}$ (a standard parabola opening upwards with vertex at the origin).

Step3: Apply the reflection

Substitute $-x$ into $f(x)$. Since $f(x)=x^{2}$, then $g(x)=f(-x)=(-x)^{2}$. And $(-x)^{2}=x^{2}$.

Answer:

$g(x)=x^{2}$