Precalculus Examples

$f (x) = 2^{x - 1}$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = 2^{x - 1}$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $2^{x - 1} = 0$ .

$2^{x - 1} = 0$

Step 1.2.2

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

$\ln (2^{x - 1}) = \ln (0)$

Step 1.2.3

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 1.2.4

There is no solution for $2^{x - 1} = 0$

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.

Tap for more steps...

Step 2.1

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

$y = 2^{(0) - 1}$

Step 2.2

Simplify $2^{(0) - 1}$ .

Tap for more steps...

Step 2.2.1

Subtract $1$ from $0$ .

$y = 2^{- 1}$

Step 2.2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{2})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \frac{1}{2})$

Step 4