Question

which of the following are the characteristics for the graph of the parent linear function? select all that apply. (1 point) the domain and range are $(-infty, infty)$. it is an even function. it decreases over the interval $(-infty, infty)$. the end behavior is $f(x) \to infty$ as $x \to infty$ and $f(x) \to -infty$ as $x \to -infty$.

Explanation:

Step1: Define parent linear function

The parent linear function is $f(x) = x$.

Step2: Analyze domain and range

For $f(x)=x$, $x$ can be any real number, so domain is $(-\infty,\infty)$. The output $f(x)$ also covers all real numbers, so range is $(-\infty,\infty)$.

Step3: Check if it's an even function

An even function satisfies $f(-x)=f(x)$. Here, $f(-x)=-x
eq f(x)=x$, so it is not even.

Step4: Check if it decreases over $(-\infty,\infty)$

The slope of $f(x)=x$ is $1>0$, so it increases, not decreases, over $(-\infty,\infty)$.

Step5: Analyze end behavior

As $x \to \infty$, $f(x)=x \to \infty$. As $x \to -\infty$, $f(x)=x \to -\infty$.

Answer:

• The domain and range are $(-\infty,\infty)$.
• The end behavior is $f(x) \to \infty$ as $x \to \infty$ and $f(x) \to -\infty$ as $x \to -\infty$.