Find the x and y Intercepts g(x)=-5^x+5

$g (x) = - 5^{x} + 5$

Find the x-intercepts.

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

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

Solve the equation.

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

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

Subtract $5$ from both sides of the equation.

$- 5^{x} = - 5$

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

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

$\frac{- 5^{x}}{- 1} = \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{5^{x}}{1} = \frac{- 5}{- 1}$

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

$5^{x} = \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$5^{x} = 5$

Create equivalent expressions in the equation that all have equal bases.

$5^{x} = 5^{1}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = 1$

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Find the y-intercepts.

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

$y = - 5^{0} + 5$

Simplify $- 5^{0} + 5$ .

Simplify each term.

Anything raised to $0$ is $1$ .

$y = - 1 \cdot 1 + 5$

Multiply $- 1$ by $1$ .

$y = - 1 + 5$

Add $- 1$ and $5$ .

$y = 4$

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

List the intersections.

x-intercept(s): $(1, 0)$

y-intercept(s): $(0, 4)$