Key Characteristics of Functions

What is the y-intercept of the function?

• 2

• 3

• 1

• -2

Answer explanation

The y-intercept of the function is the value of the function when x=0. Therefore, the y-intercept is 3, as the function evaluates to 3 when x=0.

Identify the y-intercept (initial value) of the function f(x)=2(4)^x.

• 2

• 4

• (2)^x

• 8

Answer explanation

The y-intercept (initial value) of the function f(x)=2(4)^x is 2, as it represents the value of the function when x=0.

Given the function, f(x) = 6.5(0.85)^x, identify the growth/decay rate.

• 6.5

• 0.85

• x

• f(x)

Answer explanation

The growth/decay rate is identified by the base of the exponential function, which is 0.85 in this case. Therefore, the correct choice is 0.85.

What is the maximum height?

• 200

• 50

• 3

• 0

Answer explanation

The correct choice for the maximum height is 200, as it is the highest value among the options provided.

What is the y-intercept?

• (6, 0)

• (0, 6)

• (-3, 0)

• (0, -3)

Answer explanation

The y-intercept is the point where the graph intersects the y-axis. In this case, the y-intercept is at (0, -3), which means the y-coordinate is -3 when x is 0.

What are the green dots called?

• y-intercepts

• maximum

• minimum

• x-intercepts

Answer explanation

The green dots are called x-intercepts, which are the points where the graph intersects the x-axis.

Looking at this graph, what is the x-intercept?

• (4, 0)

• (0, 4)

• (-2, 0)

• (0, -2)

Answer explanation

The x-intercept is where the graph crosses the x-axis, which is at (-2, 0) in this case.

Name the vertex to the given quadratic graph

• (2,3)

• (3,2)

• (0,-1)

• (4,-1)

Answer explanation

The vertex of the quadratic graph is (2,3) as it represents the maximum or minimum point of the parabola.

Identify the y-intercept.

• (0,3)

• (3,0)

• (1,0)

• (2,-1)

Answer explanation

The y-intercept is the point where the graph crosses the y-axis. In this case, the y-intercept is (0,3) because the y-coordinate is 3 when x=0.

Write a quadratic equation given the x intercepts and one other point.

Step 1: Write the factors.

The intercepts of this function are (6, 0) and (8, 0). Write the factors.

• (x-6) and (x-8)

• (x+6) and (x+8)

• (x-6) and (x+8)

• (x+6) and (x-8)

Answer explanation

The correct factors for the x-intercepts (6, 0) and (8, 0) are (x-6) and (x-8), respectively.