Find the x and y Intercepts h(x)=81-3^(x+1)

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

Subtract $81$ from both sides of the equation.

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

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

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

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

Simplify the right side.

Divide $- 81$ by $- 1$ .

$3^{x + 1} = 81$

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

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

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

$x + 1 = 4$

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

Subtract $1$ from both sides of the equation.

$x = 4 - 1$

Subtract $1$ from $4$ .

$x = 3$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

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

Simplify each term.

Add $0$ and $1$ .

$y = 81 - 3^{1}$

Evaluate the exponent.

$y = 81 - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$y = 81 - 3$

Subtract $3$ from $81$ .

$y = 78$

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

Find the x and y Intercepts h(x)=81-3^(x+1)

Related Questions

Support LCMGCF.com by disabling your adblocker.