Graphing Exponential Functions

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Math › Graphing Exponential Functions

Questions 1 - 4

1

Find the -intercept(s) of $y=\frac{x^2+9x+8}{x^2-44}$ .

and

and

$x=\frac{1}{8}$

$x=2\sqrt{2}$

$x=2\sqrt{11}$

Explanation

To find the -intercept(s) of $y=\frac{x^2+9x+8}{x^2-44}$ , we need to set the numerator equal to zero and solve.

First, notice that can be factored into . Now set that equal to zero: .

Since we have two sets in parentheses, there are two separate values that can cause our equation to equal zero: one where and one where .

Solve for each value:

and

.

Therefore there are two -interecpts: and .

2

Find the -intercept(s) of $y=\frac{x^3+2x+8}{x^2-36}$ .

$y=-\frac{2}{9}$

$y=\frac{2}{9}$

This function does not cross the -axis.

Explanation

To find the -intercept, set in the equation and solve.

$y=\frac{x^3+2x+8}{x^2-36}$

$y=\frac{(0)^3+2(0)+8}{(0)^2-36}$

$y=\frac{(0)+(0)+8}{(0)-36}$

$y=\frac{8}{-36}$

$y=-\frac{2}{9}$

3

Find the -intercept(s) of $y=\frac{x^3+2x+8}{x^2-36}$ .

The function does not cross the -axis.

or

Explanation

To find the -intercept(s) of $y=\frac{x^3+2x+8}{x^2-36}$ , we need to set the numerator equal to zero.

That means .

The best way to solve for a funky equation like this is to graph it in your calculator and calculate the roots. The result is $x\approx -1.67$ .

4

Find the -intercept(s) of $y=\frac{x^2+9x+8}{x^2-44}$ .

$y=-\frac{2}{11}$

$y=2\sqrt{11}$

and

$y=\frac{2}{11}$

$y=5\tfrac{1}{2}$

Explanation

To find the -intercept(s) of $y=\frac{x^2+9x+8}{x^2-44}$ , set the value equal to zero and solve.

$y=\frac{x^2+9x+8}{x^2-44}$

$y=\frac{(0)^2+9(0)+8}{(0)^2-44}$

$y=\frac{(0)+(0)+8}{(0)-44}$

$y=\frac{8}{-44}$

$y=-\frac{2}{11}$

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