Understanding Vertical Intercepts

This video tutorial explains how to identify and calculate the vertical intercepts of various functions, including quadratic, linear, square root, cube root, constant, cubic, rational, identity, and absolute value functions. The vertical intercept, or y-intercept, is the point where a graph crosses the vertical axis, and it is found by setting the input (x) to zero and solving for the output (y). The tutorial provides examples and visual graphs to illustrate the concept, highlighting cases where the intercept is real or non-existent.

What is the vertical intercept of a function?

• The lowest point on the graph

• The point where the graph crosses the horizontal axis

• The point where the graph crosses the vertical axis

• The highest point on the graph

How do you find the vertical intercept of a function?

• Find the minimum value of the function

• Find the maximum value of the function

• Set the input value to zero

• Set the output value to zero

For the function f(x) = x^2 + 3x - 10, what is the vertical intercept?

• (-10, 0)

• (10, 0)

• (0, 10)

• (0, -10)

What is the vertical intercept of the linear function f(x) = 5x + 7?

• (7, 0)

• (0, 5)

• (5, 0)

• (0, 7)

Why does the function f(x) = sqrt(2x - 8) have no vertical intercept?

• The radicand is positive

• The radicand is zero

• The radicand is negative

• The function is not defined

What is the vertical intercept of the cube root function f(x) = cube root(4x - 6)?

• (0, -6)

• (0, cube root of -6)

• (0, cube root of 6)

• (0, 6)

For the constant function f(x) = 19, what is the vertical intercept?

• (19, 0)

• (0, 0)

• (0, 19)

• (0, -19)

What is the vertical intercept of the cubic function f(x) = x^3 - 4x?

• (0, 4)

• (4, 0)

• (0, 0)

• (0, -4)

For the rational function f(x) = (x + 1) / (x - 6), what is the vertical intercept?

• (0, 1/6)

• (0, -1/6)

• (1/6, 0)

• (-1/6, 0)

What is the vertical intercept of the absolute value function f(x) = |x - 3|?

• (-3, 0)

• (3, 0)

• (0, 3)

• (0, -3)