Algebra Examples

$g (x) = - 5^{x} + 5$

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 $x$ .

$0 = - 5^{x} + 5$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- 5^{x} + 5 = 0$ .

$- 5^{x} + 5 = 0$

Step 1.2.2

Subtract $5$ from both sides of the equation.

$- 5^{x} = - 5$

Step 1.2.3

Divide each term in $- 5^{x} = - 5$ by $- 1$ and simplify.

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Step 1.2.3.1

Divide each term in $- 5^{x} = - 5$ by $- 1$ .

$\frac{- 5^{x}}{- 1} = \frac{- 5}{- 1}$

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.

$\frac{5^{x}}{1} = \frac{- 5}{- 1}$

Step 1.2.3.2.2

Divide $5^{x}$ by $1$ .

$5^{x} = \frac{- 5}{- 1}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $- 5$ by $- 1$ .

$5^{x} = 5$

Step 1.2.4

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

$5^{x} = 5^{1}$

Step 1.2.5

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

$x = 1$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

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 $y$ .

$y = - 5^{0} + 5$

Step 2.2

Simplify $- 5^{0} + 5$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Anything raised to $0$ is $1$ .

$y = - 1 \cdot 1 + 5$

Step 2.2.1.2

Multiply $- 1$ by $1$ .

$y = - 1 + 5$

Step 2.2.2

Add $- 1$ and $5$ .

$y = 4$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

Step 3

List the intersections.

x-intercept(s): $(1, 0)$

y-intercept(s): $(0, 4)$

Step 4