Algebra Examples

f (x) = 5 {(3)}^{x}

$f (x) = 5 {(3)}^{x}$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

0 = 5 {(3)}^{x}

$0 = 5 {(3)}^{x}$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as

5 \cdot 3^{x} = 0

$5 \cdot 3^{x} = 0$ .

5 \cdot 3^{x} = 0

$5 \cdot 3^{x} = 0$

Step 1.2.2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

\ln (5 \cdot 3^{x}) = \ln (0)

$\ln (5 \cdot 3^{x}) = \ln (0)$

Step 1.2.3

The equation cannot be solved because

\ln (0)

$\ln (0)$ is undefined.

Undefined

Step 1.2.4

There is no solution for

5 \cdot 3^{x} = 0

$5 \cdot 3^{x} = 0$

No solution

No solution

Step 1.3

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

x-intercept(s):

None

$None$

x-intercept(s):

None

$None$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

y = 5 {(3)}^{0}

$y = 5 {(3)}^{0}$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

y = 5 \cdot 3^{0}

$y = 5 \cdot 3^{0}$

Step 2.2.2

Remove parentheses.

y = 5 {(3)}^{0}

$y = 5 {(3)}^{0}$

Step 2.2.3

Simplify

5 {(3)}^{0}

$5 {(3)}^{0}$ .

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Step 2.2.3.1

Anything raised to

0

$0$ is

1

$1$ .

y = 5 \cdot 1

$y = 5 \cdot 1$

Step 2.2.3.2

Multiply

5

$5$ by

1

$1$ .

y = 5

$y = 5$

y = 5

$y = 5$

y = 5

$y = 5$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

(0, 5)

$(0, 5)$

y-intercept(s):

(0, 5)

$(0, 5)$

Step 3

List the intersections.

x-intercept(s):

None

$None$

y-intercept(s):

(0, 5)

$(0, 5)$

Step 4

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$