Algebra Examples

$y = 4 (2^{x}) - 2$

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 $x$ .

$0 = 4 (2^{x}) - 2$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $4 \cdot 2^{x} - 2 = 0$ .

$4 \cdot 2^{x} - 2 = 0$

Step 1.2.2

Multiply $4 \cdot 2^{x}$ .

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Step 1.2.2.1

Rewrite $4$ as $2^{2}$ .

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

Step 1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{2 + x} - 2 = 0$

Step 1.2.3

Add $2$ to both sides of the equation.

$2^{2 + x} = 2$

Step 1.2.4

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

$2^{2 + x} = 2^{1}$

Step 1.2.5

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

$2 + x = 1$

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 $2$ from both sides of the equation.

$x = 1 - 2$

Step 1.2.6.2

Subtract $2$ from $1$ .

$x = - 1$

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 $y$ .

$y = 4 (2^{0}) - 2$

Step 2.2

Solve the equation.

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Step 2.2.1

Multiply $4$ by $2^{0}$ .

$y = 4 \cdot 2^{0} - 2$

Step 2.2.2

Remove parentheses.

$y = 4 (2^{0}) - 2$

Step 2.2.3

Simplify $4 (2^{0}) - 2$ .

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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 $1$ .

$y = 4 \cdot 1 - 2$

Step 2.2.3.1.2

Multiply $4$ by $1$ .

$y = 4 - 2$

Step 2.2.3.2

Subtract $2$ from $4$ .

$y = 2$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4