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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

Simplify the expression.

Apply the product rule to $\frac{1}{2}$ .

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

One to any power is one.

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

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

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

Set the numerator equal to zero.

$2 = 0$

Since $2 \neq 0$ , there are no solutions.

No solution

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

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

Simplify the expression.

Apply the product rule to $\frac{1}{2}$ .

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

Anything raised to $0$ is $1$ .

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

Anything raised to $0$ is $1$ .

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

Cancel the common factor of $1$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 2 \cdot 1$

Multiply $2$ by $1$ .

$y = 2$

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

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

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