Trigonometry Examples

$y = 3^{x} - 3$

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 $x$ .

$0 = 3^{x} - 3$

Step 1.2

Solve the equation.

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Step 1.2.1

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

$3^{x} - 3 = 0$

Step 1.2.2

Add $3$ to both sides of the equation.

$3^{x} = 3$

Step 1.2.3

Create equivalent expressions in the equation that all have equal bases.

$3^{x} = 3^{1}$

Step 1.2.4

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = 1$

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 $y$ .

$y = 3^{0} - 3$

Step 2.2

Simplify $3^{0} - 3$ .

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Step 2.2.1

Anything raised to $0$ is $1$ .

$y = 1 - 3$

Step 2.2.2

Subtract $3$ from $1$ .

$y = - 2$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 2)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 2)$

Step 4