Find the x and y Intercepts f(x)=3(0.2)^x+2

$f (x) = 3 {(0.2)}^{x} + 2$

Find the x-intercepts.

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

$0 = 3 {(0.2)}^{x} + 2$

Solve the equation.

Rewrite the equation as $3 \cdot {0.2}^{x} + 2 = 0$ .

$3 \cdot {0.2}^{x} + 2 = 0$

Subtract $2$ from both sides of the equation.

$3 \cdot {0.2}^{x} = - 2$

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

$\ln (3 \cdot {0.2}^{x}) = \ln (- 2)$

The equation cannot be solved because $\ln (- 2)$ is undefined.

Undefined

There is no solution for $3 \cdot {0.2}^{x} = - 2$

No solution

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

x-intercept(s): $None$

Find the y-intercepts.

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

$y = 3 {(0.2)}^{0} + 2$

Solve the equation.

Remove parentheses.

$y = 3 \cdot {0.2}^{0} + 2$

Remove parentheses.

$y = 3 {(0.2)}^{0} + 2$

Simplify $3 {(0.2)}^{0} + 2$ .

Simplify each term.

Anything raised to $0$ is $1$ .

$y = 3 \cdot 1 + 2$

Multiply $3$ by $1$ .

$y = 3 + 2$

Add $3$ and $2$ .

$y = 5$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $None$

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