Chapter 4.7, Problem 32E

To determine

To find: the real zeroes of the function and describe transformation of the graph $f$ that results in the graph of $g$ .

Answer to Problem 32E

The zeroes of Black curve are at $x=-2,0,2$ and that of blue curve is at $x=0,2,4$ and graph of blue is shifted towards the right in the difference of two unit.

Explanation of Solution

Given:

  

Concept used:

The no of zeroes or root the function can be derived from the graph as the number of cut the curve made with horizontal $x$ axis it is also called roots or the solution of the equation.

Calculation:

According to the given graph:

There is a two curve one is black and one is black.

The no of zeroes or root the function can be derived from the graph as the number of cut the curve made with horizontal $x$ axis.

The black curve and blue both curves cut the $x$ axis at four points but different point.

Black curve cut the $x$ axis at $\left(-2,0\right),\left(0,0\right),\left(2,0\right)$ and similarly blue curve cut the $x$ axis at $\left(0,0\right),\left(2,0\right),\left(4,0\right)$ .

Since, the graph of blue is shifted towards the right in the difference of two unit.

Hence, the zeroes of Black curve are at $x=-2,0,2$ and that of blue curve is at $x=0,2,4$ and graph of blue is shifted towards the right in the difference of two unit.

Calculation: