Find the x and y Intercepts g(x)=2((1^x)/3)+1

$g (x) = 2 (\frac{1^{x}}{3}) + 1$

Step 1

Find the x-intercepts.

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

$0 = 2 (\frac{1^{x}}{3}) + 1$

Solve the equation.

Rewrite the equation as $2 (\frac{1^{x}}{3}) + 1 = 0$ .

$2 (\frac{1^{x}}{3}) + 1 = 0$

Simplify $2 (\frac{1^{x}}{3}) + 1$ .

Simplify each term.

One to any power is one.

$2 (\frac{1}{3}) + 1 = 0$

Combine $2$ and $\frac{1}{3}$ .

$\frac{2}{3} + 1 = 0$

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$\frac{2}{3} + \frac{3}{3} = 0$

Combine the numerators over the common denominator.

$\frac{2 + 3}{3} = 0$

Add $2$ and $3$ .

$\frac{5}{3} = 0$

Set the numerator equal to zero.

$5 = 0$

Since $5 \neq 0$ , there are no solutions.

No solution

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.

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

$y = 2 (\frac{1^{0}}{3}) + 1$

Solve the equation.

Multiply $2$ by $\frac{1^{0}}{3}$ .

$y = 2 (\frac{1^{0}}{3}) + 1$

Simplify $2 (\frac{1^{0}}{3}) + 1$ .

Simplify each term.

Anything raised to $0$ is $1$ .

$y = 2 (\frac{1}{3}) + 1$

Combine $2$ and $\frac{1}{3}$ .

$y = \frac{2}{3} + 1$

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$y = \frac{2}{3} + \frac{3}{3}$

Combine the numerators over the common denominator.

$y = \frac{2 + 3}{3}$

Add $2$ and $3$ .

$y = \frac{5}{3}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{5}{3})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \frac{5}{3})$

Step 4

Find the x and y Intercepts g(x)=2((1^x)/3)+1

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