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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

Multiply both sides of the equation by $2$ .

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

Simplify both sides of the equation.

Simplify the left side.

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Multiply $2$ by $0$ .

$6^{x} = 0$

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

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

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

Undefined

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

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 $y$ .

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

Solve the equation.

Multiply $\frac{1}{2}$ by $6^{0}$ .

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

Remove parentheses.

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

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

Anything raised to $0$ is $1$ .

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

Multiply $\frac{1}{2}$ by $1$ .

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

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{2})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \frac{1}{2})$

Step 4

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

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