Find the x and y Intercepts f(x)=5*(1/6)^x

$f (x) = 5 \cdot {(\frac{1}{6})}^{x}$

Find the x-intercepts.

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

$0 = 5 \cdot {(\frac{1}{6})}^{x}$

Solve the equation.

Rewrite the equation as $5 \cdot {(\frac{1}{6})}^{x} = 0$ .

$5 \cdot {(\frac{1}{6})}^{x} = 0$

Simplify $5 \cdot {(\frac{1}{6})}^{x}$ .

Simplify the expression.

Apply the product rule to $\frac{1}{6}$ .

$5 \cdot \frac{1^{x}}{6^{x}} = 0$

One to any power is one.

$5 \cdot \frac{1}{6^{x}} = 0$

Combine $5$ and $\frac{1}{6^{x}}$ .

$\frac{5}{6^{x}} = 0$

Set the numerator equal to zero.

$5 = 0$

Since $5 \neq 0$ , there are no solutions.

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 $y$ .

$y = 5 \cdot {(\frac{1}{6})}^{0}$

Solve the equation.

Remove parentheses.

$y = 5 \cdot {(\frac{1}{6})}^{0}$

Simplify $5 \cdot {(\frac{1}{6})}^{0}$ .

Simplify the expression.

Apply the product rule to $\frac{1}{6}$ .

$y = 5 \cdot \frac{1^{0}}{6^{0}}$

Anything raised to $0$ is $1$ .

$y = 5 \cdot \frac{1}{6^{0}}$

Anything raised to $0$ is $1$ .

$y = 5 \cdot \frac{1}{1}$

Cancel the common factor of $1$ .

Cancel the common factor.

$y = 5 \cdot \frac{1}{1}$

Rewrite the expression.

$y = 5 \cdot 1$

Multiply $5$ by $1$ .

$y = 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5)$

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, 5)$

Find the x and y Intercepts f(x)=5*(1/6)^x

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