Find the x and y Intercepts -3^(x+5)-9

$- 3^{x + 5} - 9$

Step 1

Write $- 3^{x + 5} - 9$ as an equation.

$y = - 3^{x + 5} - 9$

Step 2

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - 3^{x + 5} - 9$

Solve the equation.

Rewrite the equation as $- 3^{x + 5} - 9 = 0$ .

$- 3^{x + 5} - 9 = 0$

Add $9$ to both sides of the equation.

$- 3^{x + 5} = 9$

Divide each term in $- 3^{x + 5} = 9$ by $- 1$ and simplify.

Divide each term in $- 3^{x + 5} = 9$ by $- 1$ .

$\frac{- 3^{x + 5}}{- 1} = \frac{9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{3^{x + 5}}{1} = \frac{9}{- 1}$

Divide $3^{x + 5}$ by $1$ .

$3^{x + 5} = \frac{9}{- 1}$

Simplify the right side.

Divide $9$ by $- 1$ .

$3^{x + 5} = - 9$

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (3^{x + 5}) = \ln (- 9)$

The equation cannot be solved because $\ln (- 9)$ is undefined.

Undefined

There is no solution for $3^{x + 5} = - 9$

No solution

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 3

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - 3^{(0) + 5} - 9$

Simplify $- 3^{(0) + 5} - 9$ .

Simplify each term.

Add $0$ and $5$ .

$y = - 3^{5} - 9$

Raise $3$ to the power of $5$ .

$y = - 1 \cdot 243 - 9$

Multiply $- 1$ by $243$ .

$y = - 243 - 9$

Subtract $9$ from $- 243$ .

$y = - 252$

y-intercept(s) in point form.

y-intercept(s): $(0, - 252)$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - 252)$

Step 5

Find the x and y Intercepts -3^(x+5)-9

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