Question

consider the following function. (h(x)=\frac{7}{4}x^{3}) step 1 of 2: identify the general shape of the graph of this function.

Explanation:

Step1: Analyze the function degree

The function $h(x)=\frac{7}{4}x^{3}$ is a cubic function. Cubic functions have the general form $y = ax^{3}+bx^{2}+cx + d$, and in this case $b = 0$, $c = 0$, $d = 0$ and $a=\frac{7}{4}>0$.

Step2: Recall cubic - function shape

For a cubic function $y = ax^{3}+bx^{2}+cx + d$ with $a>0$, as $x\to-\infty$, $y\to-\infty$ and as $x\to+\infty$, $y\to+\infty$. The general shape is an S - shaped curve.

Answer:

An S - shaped curve.