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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.

Sagot :

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

[tex]\sf f(x)=\begin{cases}\sf (x+2)²,x\neq \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}[/tex]

  • 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

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