Chapter 1.1, Problem 4E

To determine

To identify: The family to which $f$ belongs and then to compare the graph of $f$ to graph of its parent function.

Answer to Problem 4E

  $f$ is a quadratic function.

Explanation of Solution

Given information: Graph of function $f(x)=-2x^2+3$ .

As the graph is kind of U-shaped, $f$ is a quadratic function.

Graph of parent quadratic function is like:

  

Comparing given function with parent function $g(x)=x^2$ , the given function is vertically translated $3$ units upward and is also vertically stretched, it is narrower and gets broad not as fast as the parent quadratic function, further it is reflected over the $x-axis$ with respect to parent function. Its domain is all real numbers but the range of $f(x)$ is $y\le 3$ , whereas the range of parent function is $y\ge 0$ .