Find the Vertical and Horizontal Intercept(s) f(x)=5(3)^x

$f (x) = 5 {(3)}^{x}$

Step 1

Find the x-intercepts.

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

$0 = 5 {(3)}^{x}$

Solve the equation.

Rewrite the equation as $5 \cdot 3^{x} = 0$ .

$5 \cdot 3^{x} = 0$

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

$\ln (5 \cdot 3^{x}) = \ln (0)$

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

There is no solution for $5 \cdot 3^{x} = 0$

No solution

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

$y = 5 {(3)}^{0}$

Solve the equation.

Remove parentheses.

$y = 5 \cdot 3^{0}$

Remove parentheses.

$y = 5 {(3)}^{0}$

Simplify $5 {(3)}^{0}$ .

Anything raised to $0$ is $1$ .

$y = 5 \cdot 1$

Multiply $5$ by $1$ .

$y = 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 5)$

Step 4