Algebra Examples

$h (x) = 2 (3^{x}) - 18$

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 $x$ .

$0 = 2 (3^{x}) - 18$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $2 \cdot 3^{x} - 18 = 0$ .

$2 \cdot 3^{x} - 18 = 0$

Step 1.2.2

Add $18$ to both sides of the equation.

$2 \cdot 3^{x} = 18$

Step 1.2.3

Divide each term in $2 \cdot 3^{x} = 18$ by $2$ and simplify.

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Step 1.2.3.1

Divide each term in $2 \cdot 3^{x} = 18$ by $2$ .

$\frac{2 \cdot 3^{x}}{2} = \frac{18}{2}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $2$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{2 \cdot 3^{x}}{2} = \frac{18}{2}$

Step 1.2.3.2.1.2

Divide $3^{x}$ by $1$ .

$3^{x} = \frac{18}{2}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $18$ by $2$ .

$3^{x} = 9$

Step 1.2.4

Create equivalent expressions in the equation that all have equal bases.

$3^{x} = 3^{2}$

Step 1.2.5

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = 2$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

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 $y$ .

$y = 2 (3^{0}) - 18$

Step 2.2

Solve the equation.

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Step 2.2.1

Multiply $2$ by $3^{0}$ .

$y = 2 \cdot 3^{0} - 18$

Step 2.2.2

Remove parentheses.

$y = 2 (3^{0}) - 18$

Step 2.2.3

Simplify $2 (3^{0}) - 18$ .

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Anything raised to $0$ is $1$ .

$y = 2 \cdot 1 - 18$

Step 2.2.3.1.2

Multiply $2$ by $1$ .

$y = 2 - 18$

Step 2.2.3.2

Subtract $18$ from $2$ .

$y = - 16$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 16)$

Step 3

List the intersections.

x-intercept(s): $(2, 0)$

y-intercept(s): $(0, - 16)$

Step 4