Chapter 10, Problem 1CR

To determine

To graph the function and find Domain, Range.

Answer to Problem 1CR

Domain = $[0,\infty )$

Range = $[7,\infty )$

Explanation of Solution

Given information: $g\left(x\right)=\sqrt{x}+7$

Formula Used: Square root function cannot be negative.

Calculation:

  $g\left(x\right)=\sqrt{x}+7$

As the domain of square root function is greater than or equal to zero i.e. cannot be negative.

So,

  $\sqrt{x}\ge 0$

Squaring both sides,

  $x\ge 0$

Hence,

Domain = $[0,\infty )$

As,

  $\sqrt{x}\ge 0$

Now, Add 7 both sides

  $\sqrt{x}+7\ge 0+7$

So,

  $\sqrt{x}+7\ge 7$

As, $g\left(x\right)=\sqrt{x}+7$

  $g\left(x\right)\ge 7$

Range = $[7,\infty )$

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis.

Parent function: $f\left(x\right)=\sqrt{x}$

Horizontal shift: none

Vertical shift: up 7 units

Stretch or shrink: none.