Chapter 1.1, Problem 53E

a.

To determine

To compare: Each function with it parent function and then determine its translational characteristic.

Answer to Problem 53E

It is a vertical translation.

Explanation of Solution

Given Information: Function is $f(x)=2\left|x\right|-3$ .

Parent function $g(x)=\left|x\right|$ has one term, but the given term has one additional separate term i.e. $3$ . Thus, it is a vertical translation.

b.

To determine

To compare: Each function with it parent function and then determine its translational characteristic.

Answer to Problem 53E

  $f$ is a horizontal translation.

Explanation of Solution

Given Information: Function is $f(x)={(x-8)}^2$ .

The parent function is $g(x)=x^2$ , in the given function 8 is subtracted from within the variable part, it is inside the brackets, that means this is a horizontal translation.

Thus, $f$ is a horizontal translation.

c.

To determine

To compare: Each function with it parent function and then determine its translational characteristic.

Answer to Problem 53E

  $f$ is a vertical and horizontal translation.

Explanation of Solution

Given Information: Function is $f(x)=\left|x+2\right|+4$ .

Parent function $g(x)=\left|x\right|$ has one term, but the given term has one additional separate term i.e. $4$ Moreover, there is an addition of $2$ within the vertical lines along with variable part, this implies that there is horizontal translation too.

Thus, $f$ is a vertical and horizontal translation.

d.

To determine

To compare: Each function with it parent function and then determine its translational characteristic.

Answer to Problem 53E

There is no translation.

Explanation of Solution

Given Information: Function is $f(x)=4x^2$ .

No other term is added in the parent function $g(x)=x^2$ , the variable part in the given function is also the same without any modification (addition or subtraction).

Thus, there is no translation.