Chapter 1.7, Problem 43E

(a)

To determine

To draw:

The graph of the function

Explanation of Solution

Given:

  $y=\sqrt{x-9}$

  

(b)

To determine

To find:

The domain of $f\left(x\right)=y=\sqrt{x-9}$

Answer to Problem 43E

The domain of $\left(-\infty ,9\right]$ , Range $\left[0,\infty \right)$

Explanation of Solution

Given:

  $f\left(x\right)=y=\sqrt{x-9}$

Concept used:

The graph of $f$ is increasing with respect to the y-axis

Calculation:

The smallest number that the square root of that is still in the real number system, which of course is zero

Solved the equation $y=\sqrt{x-9}$ = 0

This is

  $x=9$

So, that is the smallest, legal x value which is the lower limit of domain

There is no maximum x value so the upper limit of domain is positive infinity

So, domain $\left(-\infty ,9\right]$

Range $\left[0,\infty \right)$

(c)

To determine

To draw:

The graph of the function

Explanation of Solution

Given:

  $y=\sqrt{x-9}$

Concept used:

The graph of $f$ is increasing with respect to the y-axis

The graph of the equation is

  $y=x^3$

The function is odd

The graph has an intercept at $\left(0,0\right)$

The graph is increasing on the interval $\left(-\infty ,\infty \right)$

The is symmetric with respect to the origin

$x-axis$	$9$	$11$	$10$	$12$
$y-axis$	$0$	$1.41$	$1$	$1.73$

The set of all y-values that a function passes through.also the right coordinate in a coordinate pair