Precalculus Examples

$y = 4 \cdot {(\frac{1}{2})}^{x}$

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 $x$ .

$0 = 4 \cdot {(\frac{1}{2})}^{x}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $4 \cdot {(\frac{1}{2})}^{x} = 0$ .

$4 \cdot {(\frac{1}{2})}^{x} = 0$

Step 1.2.2

Simplify $4 \cdot {(\frac{1}{2})}^{x}$ .

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Step 1.2.2.1

Simplify the expression.

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Step 1.2.2.1.1

Apply the product rule to $\frac{1}{2}$ .

$4 \cdot \frac{1^{x}}{2^{x}} = 0$

Step 1.2.2.1.2

One to any power is one.

$4 \cdot \frac{1}{2^{x}} = 0$

Step 1.2.2.2

Combine $4$ and $\frac{1}{2^{x}}$ .

$\frac{4}{2^{x}} = 0$

Step 1.2.3

Set the numerator equal to zero.

$4 = 0$

Step 1.2.4

Since $4 \neq 0$ , there are no solutions.

No solution

Step 1.3

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

x-intercept(s): $None$

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 $y$ .

$y = 4 \cdot {(\frac{1}{2})}^{0}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

$y = 4 \cdot {(\frac{1}{2})}^{0}$

Step 2.2.2

Simplify $4 \cdot {(\frac{1}{2})}^{0}$ .

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Step 2.2.2.1

Simplify the expression.

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Step 2.2.2.1.1

Apply the product rule to $\frac{1}{2}$ .

$y = 4 \cdot \frac{1^{0}}{2^{0}}$

Step 2.2.2.1.2

Anything raised to $0$ is $1$ .

$y = 4 \cdot \frac{1}{2^{0}}$

Step 2.2.2.1.3

Anything raised to $0$ is $1$ .

$y = 4 \cdot \frac{1}{1}$

Step 2.2.2.2

Cancel the common factor of $1$ .

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Step 2.2.2.2.1

Cancel the common factor.

$y = 4 \cdot \frac{1}{1}$

Step 2.2.2.2.2

Rewrite the expression.

$y = 4 \cdot 1$

Step 2.2.2.3

Multiply $4$ by $1$ .

$y = 4$

Step 2.3

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $None$

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

Step 4