Precalculus Examples

$f (x) = 3 x^{3} - 5 x + 7$

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 $x$ .

$0 = 3 x^{3} - 5 x + 7$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Remove parentheses.

$0 = 3 x^{3} - 5 x + 7$

Step 1.2.2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 1.73530678$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- 1.73530678, 0)$

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 $y$ .

$y = 3 {(0)}^{3} - 5 \cdot 0 + 7$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$y = 3 \cdot 0^{3} - 5 \cdot 0 + 7$

Step 2.2.2

Remove parentheses.

$y = 3 {(0)}^{3} - 5 \cdot 0 + 7$

Step 2.2.3

Simplify $3 {(0)}^{3} - 5 \cdot 0 + 7$ .

Tap for more steps...

Step 2.2.3.1

Simplify each term.

Tap for more steps...

Step 2.2.3.1.1

Raising $0$ to any positive power yields $0$ .

$y = 3 \cdot 0 - 5 \cdot 0 + 7$

Step 2.2.3.1.2

Multiply $3$ by $0$ .

$y = 0 - 5 \cdot 0 + 7$

Step 2.2.3.1.3

Multiply $- 5$ by $0$ .

$y = 0 + 0 + 7$

Step 2.2.3.2

Simplify by adding numbers.

Tap for more steps...

Step 2.2.3.2.1

Add $0$ and $0$ .

$y = 0 + 7$

Step 2.2.3.2.2

Add $0$ and $7$ .

$y = 7$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, 7)$

Step 3

List the intersections.

x-intercept(s): $(- 1.73530678, 0)$

y-intercept(s): $(0, 7)$

Step 4