Find the x and y Intercepts f(x)=7^(x-1)+1

$f (x) = 7^{x - 1} + 1$

Find the x-intercepts.

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

$0 = 7^{x - 1} + 1$

Solve the equation.

Rewrite the equation as $7^{x - 1} + 1 = 0$ .

$7^{x - 1} + 1 = 0$

Subtract $1$ from both sides of the equation.

$7^{x - 1} = - 1$

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

$\ln (7^{x - 1}) = \ln (- 1)$

The equation cannot be solved because $\ln (- 1)$ is undefined.

Undefined

There is no solution for $7^{x - 1} = - 1$

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 $y$ .

$y = 7^{(0) - 1} + 1$

Simplify $7^{(0) - 1} + 1$ .

Simplify each term.

Subtract $1$ from $0$ .

$y = 7^{- 1} + 1$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = \frac{1}{7} + 1$

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$y = \frac{1}{7} + \frac{7}{7}$

Combine the numerators over the common denominator.

$y = \frac{1 + 7}{7}$

Add $1$ and $7$ .

$y = \frac{8}{7}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{8}{7})$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \frac{8}{7})$