Question

Write a piecewise-defined step function f(x) that has the following characteristics:

f(x) has more than one x intercept.
The domain of f(x) is the real numbers.
The range of f(x) consists of four unique integers.

Answer 1

Here use general math mind

F(x) has more than one x inetercept .

• We shall take one quadratic function in which will give 2 intercepts(Real)

Domain is for real numbers

Four unique numbers?

• Add 4 constants for 4 unique definations and that shouldn't fall under quadratic region

Lets see

`\sf f(x)=\begin{cases}\sf (x+2)²,x\\eq \left\{0,-1,1,2,3\right\}\\ \sf 0,x=0\\ \sf 1,x=-1\\ \sf 9,x=1\\ \sf 16,x=4\\ \sf 25,x=5\end{cases}`

• Has 2 x intercepts

For -2

• y=(0)²=0
• (-2,0)

For 0 it's (0,0)

And for extra ,it's discontinuous on x=0