Algebra Examples

$h (x) = 81 - 3^{x + 1}$

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 $x$ .

$0 = 81 - 3^{x + 1}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $81 - 3^{x + 1} = 0$ .

$81 - 3^{x + 1} = 0$

Step 1.2.2

Subtract $81$ from both sides of the equation.

$- 3^{x + 1} = - 81$

Step 1.2.3

Divide each term in $- 3^{x + 1} = - 81$ by $- 1$ and simplify.

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Step 1.2.3.1

Divide each term in $- 3^{x + 1} = - 81$ by $- 1$ .

$\frac{- 3^{x + 1}}{- 1} = \frac{- 81}{- 1}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Dividing two negative values results in a positive value.

$\frac{3^{x + 1}}{1} = \frac{- 81}{- 1}$

Step 1.2.3.2.2

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

$3^{x + 1} = \frac{- 81}{- 1}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $- 81$ by $- 1$ .

$3^{x + 1} = 81$

Step 1.2.4

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

$3^{x + 1} = 3^{4}$

Step 1.2.5

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

$x + 1 = 4$

Step 1.2.6

Move all terms not containing $x$ to the right side of the equation.

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Step 1.2.6.1

Subtract $1$ from both sides of the equation.

$x = 4 - 1$

Step 1.2.6.2

Subtract $1$ from $4$ .

$x = 3$

Step 1.3

x-intercept(s) in point form.

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

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 $y$ .

$y = 81 - 3^{(0) + 1}$

Step 2.2

Simplify $81 - 3^{(0) + 1}$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Add $0$ and $1$ .

$y = 81 - 3^{1}$

Step 2.2.1.2

Evaluate the exponent.

$y = 81 - 1 \cdot 3$

Step 2.2.1.3

Multiply $- 1$ by $3$ .

$y = 81 - 3$

Step 2.2.2

Subtract $3$ from $81$ .

$y = 78$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 78)$

Step 3

List the intersections.

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

y-intercept(s): $(0, 78)$

Step 4