Find the x and y Intercepts f(x)=2^(3x+1)

$f (x) = 2^{3 x + 1}$

Step 1

Find the x-intercepts.

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

$0 = 2^{3 x + 1}$

Solve the equation.

Rewrite the equation as $2^{3 x + 1} = 0$ .

$2^{3 x + 1} = 0$

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

$\ln (2^{3 x + 1}) = \ln (0)$

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

Undefined

There is no solution for $2^{3 x + 1} = 0$

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 $y$ .

$y = 2^{3 (0) + 1}$

Simplify $2^{3 (0) + 1}$ .

Multiply $3$ by $0$ .

$y = 2^{0 + 1}$

Add $0$ and $1$ .

$y = 2^{1}$

Evaluate the exponent.

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 2)$

Step 4