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

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

Find the x-intercepts.

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

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

Solve the equation.

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

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

Simplify each term.

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

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

One to any power is one.

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

Subtract $2$ from both sides of the equation.

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

Multiply both sides by $2^{x}$ .

$\frac{1}{2^{x}} \cdot 2^{x} = - 2 \cdot 2^{x}$

Simplify.

Simplify the left side.

Cancel the common factor of $2^{x}$ .

Cancel the common factor.

$\frac{1}{2^{x}} \cdot 2^{x} = - 2 \cdot 2^{x}$

Rewrite the expression.

$1 = - 2 \cdot 2^{x}$

Simplify the right side.

Multiply $- 2 \cdot 2^{x}$ .

Factor out negative.

$1 = - (2 \cdot 2^{x})$

Raise $2$ to the power of $1$ .

$1 = - (2^{1} \cdot 2^{x})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$1 = - 2^{1 + x}$

Solve for $x$ .

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

$- 2^{1 + x} = 1$

Divide each term in $- 2^{1 + x} = 1$ by $- 1$ and simplify.

Divide each term in $- 2^{1 + x} = 1$ by $- 1$ .

$\frac{- 2^{1 + x}}{- 1} = \frac{1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{2^{1 + x}}{1} = \frac{1}{- 1}$

Divide $2^{1 + x}$ by $1$ .

$2^{1 + x} = \frac{1}{- 1}$

Simplify the right side.

Divide $1$ by $- 1$ .

$2^{1 + x} = - 1$

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

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

The equation cannot be solved because $\ln (- 1)$ is undefined.

Undefined

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

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 $y$ .

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

Solve the equation.

Remove parentheses.

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

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

Simplify each term.

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

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

Anything raised to $0$ is $1$ .

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

Anything raised to $0$ is $1$ .

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

Divide $1$ by $1$ .

$y = 1 + 2$

Add $1$ and $2$ .

$y = 3$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $None$

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

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

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