Chapter 10.5, Problem 2STP

For Exercisers 1-5, choose the correct letter.

What are the domain and range of the function $y=2\sqrt{3x+4}-5$

F. $x\ge -\frac{4}{3};y\ge -5$

G. $x\ge \frac{4}{3};y\ge -5$

H. $x\le -\frac{4}{3};y\le -5$

I. $x\ge -\frac{4}{3};y\ge 5$

To determine

To find: the domain of function and range of the function.

Answer to Problem 2STP

The domain of function is $x=-\frac{4}{3}$ and the range of the function is $y\ge -5$ .

Explanation of Solution

Given information:

The function is $y=2\sqrt{3x+4}-5$ .

Calculation: to find the domain of the function, the function is defined for all the $x$ which,

  $\begin{array}{l}3x+4\ge 0\\ x\ge -\frac{4}{3}\text{ [simplify]}\end{array}$

Thus, the domain of the function is $x\ge -\frac{4}{3}$ .

And the minimum value of function occur at $x=-\frac{4}{3}$ ,

  $y=-5$

Thus, the range of the function is

  $y\ge -5$ .