Unit 1 Task 5 Prerequisities

Find the slope of the linear function.

• m = 2

• m = 1/2

• m = -2

• m = -1/2

Answer explanation

Slope

Rate of Change

Common Difference

All mean change in y divided by change in x!

Find the y-intercept of the linear function.

• (0, 6)

• -2

• (3, 0)

• 2

Answer explanation

Y-Intercept is the point where x = 0.

Write a function to model the given line.

• f(x) = 2x + 6

• f(x) = -2x + 6

• f(x) = 6x - 2

• f(x) = 6x + 2

Answer explanation

Slope (m) = -2

Y-Intercept (b) = 6

f(x) = mx + b

Plug in!

f(x) = -2x + 6

A sunflower plant was 6 inches tall when planted and grows at a rate of 3 inches per week.

The function h(w) = 3w + 6 represents the height of the plant, h(w), after w weeks.

The point (2, 12) means the plant was ​ (a)   after ​ (b)  

• 12 inches tall
• 2 weeks
• 2 inches tall
• 12 weeks

Answer explanation

The input is number of weeks.

The output is height of the plant.

So (2, 12) means the plant was 12 inches tall after 2 weeks.

Label the intercepts of the function's graph.

a

b

y-intercept

x-intercept

Answer explanation

The x-intercept is the point where the graph crosses the x-axis...the horizontal one.

The y-intercept is the point where the graph crosses the y-axis...the vertical one.

How would you describe the slope of the function shown?

• Positive

• Negative

• Constant

• Undefined

Answer explanation

Read a function like a sentence...left to right.

As we move along the line from left to right, we are rising.

Therefore, the slope is positive.

How would you describe the graph of the function?

• Increasing

• Decreasing

• Constant

Answer explanation

Since the slope is POSITIVE, we describe the function as increasing.

When is the function positive?

• x < -1

• x > -1

• x < 1

• x > 1

Answer explanation

A function is positive when it's y-values are positive.

Think of the x-intercept as neutral...it's y-value is zero, which isn't positive or negative.

All the points to the right of x = -1 have a positive y-value.

Therefore the function is positive when x > -1.

When is the function negative?

• x < -1

• x > -1

• x < 1

• x > 1

Answer explanation

A function is negative when it's y-values are negative.

Think of the x-intercept as neutral...it's y-value is zero, which isn't positive or negative.

All the points to the left of x = -1 have a negative y-value.

Therefore the function is negative when x < -1.

What is the "default" domain for a linear function? Select both correct choices.

• All Real Numbers

• Only Positive Numbers

• (-infinity, infinity)

• x > 0

Answer explanation

Without restrictions, a linear function will increase without bound to the right, and decrease without bound to the left.

Therefore, the default domain is all reals.

In interval notation, (-infinity, infinity).