Understanding Horizontal Intercepts

This video tutorial covers the process of determining horizontal intercepts for various functions, including cube root, constant, cubic, rational, identity, and absolute value functions. It explains the method of setting the function equal to zero and solving for x, using examples to illustrate each type of function. The video also discusses the graphical verification of results.

What is the y-value of all points on the horizontal axis?

• Depends on the function

• 1

• 0

• Infinity

How do you solve for x in the equation 0 = cube root of (4x - 6)?

• Subtract 4 from both sides

• Add 6 to both sides

• Cube both sides

• Square both sides

What is the horizontal intercept of the function f(x) = 19?

• (0, 0)

• (19, 0)

• (0, 19)

• No horizontal intercept

What is the first step in factoring the equation 0 = x^3 - 4x?

• Multiply by x

• Divide by x

• Factor out the greatest common factor

• Add 4 to both sides

Which of the following is a horizontal intercept of the function f(x) = x^3 - 4x?

• (1, 0)

• (0, 0)

• (3, 0)

• (4, 0)

What is the horizontal intercept of the function f(x) = (x + 1) / (x - 6)?

• (0, 1)

• (1, 0)

• (-1, 0)

• (6, 0)

What type of function is f(x) = x?

• Identity function

• Rational function

• Constant function

• Quadratic function

What is the horizontal intercept of the identity function f(x) = x?

• (1, 0)

• (x, x)

• (0, 0)

• (0, 1)

How many horizontal intercepts does the function f(x) = |x - 3| have?

• Three

• Two

• One

• None

What are the horizontal intercepts of the function f(x) = |x - 3|?

• (3, 3) and (-3, -3)

• (0, 0) and (3, 0)

• (0, 3) and (0, -3)

• (3, 0) and (-3, 0)