Find the x and y Intercepts y=1/2(6)^(x+1)

$y = \frac{1}{2} {(6)}^{x + 1}$

Step 1

Find the x-intercepts.

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

$0 = \frac{1}{2} \cdot {(6)}^{x + 1}$

Solve the equation.

Rewrite the equation as $\frac{1}{2} \cdot 6^{x + 1} = 0$ .

$\frac{1}{2} \cdot 6^{x + 1} = 0$

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot 6^{x + 1}) = 2 \cdot 0$

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot 6^{x + 1})$ .

Combine $\frac{1}{2}$ and $6^{x + 1}$ .

$2 \frac{6^{x + 1}}{2} = 2 \cdot 0$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{6^{x + 1}}{2} = 2 \cdot 0$

Rewrite the expression.

$6^{x + 1} = 2 \cdot 0$

Simplify the right side.

Multiply $2$ by $0$ .

$6^{x + 1} = 0$

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

$\ln (6^{x + 1}) = \ln (0)$

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

Undefined

There is no solution for $6^{x + 1} = 0$

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 $y$ .

$y = \frac{1}{2} \cdot {(6)}^{(0) + 1}$

Solve the equation.

Remove parentheses.

$y = \frac{1}{2} \cdot 6^{0 + 1}$

Remove parentheses.

$y = \frac{1}{2} \cdot {(6)}^{(0) + 1}$

Simplify $\frac{1}{2} \cdot {(6)}^{(0) + 1}$ .

Add $0$ and $1$ .

$y = \frac{1}{2} \cdot 6^{1}$

Evaluate the exponent.

$y = \frac{1}{2} \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$y = \frac{1}{2} \cdot (2 (3))$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot 3)$

Rewrite the expression.

$y = 3$

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 3)$

Step 4

Find the x and y Intercepts y=1/2(6)^(x+1)

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