Algebra Examples

$s (x) = - 5 \cdot 2^{3 x + 1}$

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 $x$ .

$0 = - 5 \cdot 2^{3 x + 1}$

Step 1.2

Solve the equation.

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Step 1.2.1

Remove parentheses.

$0 = - 5 \cdot 2^{3 x + 1}$

Step 1.2.2

Graph each side of the equation. The solution is the x-value of the point of intersection.

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 $y$ .

$y = - 5 \cdot 2^{3 (0) + 1}$

Step 2.2

Simplify $- 5 \cdot 2^{3 (0) + 1}$ .

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Step 2.2.1

Multiply $3$ by $0$ .

$y = - 5 \cdot 2^{0 + 1}$

Step 2.2.2

Add $0$ and $1$ .

$y = - 5 \cdot 2^{1}$

Step 2.2.3

Evaluate the exponent.

$y = - 5 \cdot 2$

Step 2.2.4

Multiply $- 5$ by $2$ .

$y = - 10$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 10)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - 10)$

Step 4