Precalculus Examples

$f (x) = 3^{x} + 2$

Step 1

Find the x-intercepts.

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Step 1.1

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

$0 = 3^{x} + 2$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $3^{x} + 2 = 0$ .

$3^{x} + 2 = 0$

Step 1.2.2

Subtract $2$ from both sides of the equation.

$3^{x} = - 2$

Step 1.2.3

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

$\ln (3^{x}) = \ln (- 2)$

Step 1.2.4

The equation cannot be solved because $\ln (- 2)$ is undefined.

Undefined

Step 1.2.5

There is no solution for $3^{x} = - 2$

No solution

Step 1.3

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.

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Step 2.1

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

$y = 3^{0} + 2$

Step 2.2

Simplify $3^{0} + 2$ .

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Step 2.2.1

Anything raised to $0$ is $1$ .

$y = 1 + 2$

Step 2.2.2

Add $1$ and $2$ .

$y = 3$

Step 2.3

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