Trigonometry Examples

$3^{y} = x$

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 $x$ .

$3^{0} = x$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $x = 3^{0}$ .

$x = 3^{0}$

Step 1.2.2

Anything raised to $0$ is $1$ .

$x = 1$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

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 $y$ .

$3^{y} = 0$

Step 2.2

Solve the equation.

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Step 2.2.1

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

$\ln (3^{y}) = \ln (0)$

Step 2.2.2

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

Undefined

Step 2.2.3

There is no solution for $3^{y} = 0$

No solution

Step 2.3

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

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(1, 0)$

y-intercept(s): $None$

Step 4