Direct Variation Scatter Plots & Lines of Best Fit Absolute Value Functions Piecewise Functions Linear Inequalities in Two Variables

The variables x and y vary directly and y = -6 when x = ¼. Write an equation that relates the variables.

y = -24x

For the graph below, tell whether y varies directly with x. If so, give an equation for the graph.

no

In the graph below, tell whether y varies directly with x. If so, give an equation for the graph.

Yes; y = 2/3x

Tell whether the following data show direct variation. If so, give the constant of variation. Time (hours) Temperature (degrees C)271722

Yes; a = 1

A truck with a capacity of 1000 pounds is being filled with mulch at a rate of 80 pounds per minute. Write a direct variation equation that gives the weight w of the mulch after t minutes.

w = 80t

For the data given below, find the equation for the best-fitting line.

y = 0.609x

For the scatter plot shown below, state whether x and y have positive correlation, negative correlation, or no correlation.

Positive correlation

For the data given, approximate the equation of the best-fitting line. x y45476

y = 0.239x

For the following data, make a scatter plot and then find the best-fitting line for the data. x y

y = 0.471x

The table below gives the average life expectancy (in years) of a person based on various years of birth. Write an equation that approximates the best- fitting line, and use it to predict the life expectancy for someone born in (Assume x represents the number of years since 1910.) Year of birth Life expectancy (years)

y = 0.317x ; in 2010 (x = 100) life expectancy will be 83 years

Sketch the parent graph along with its translation graph: y = abs(x – 5) – 4

Find the vertex of the graph: y = –abs(x) + 4

(0,4)

Sketch the graph of the function: y = –abs(x – 2) – 1

Let y = 3 abs(x – 4) + 6. Explain how the parent graph of abs(x) is translated. What is the new vertex? Is the translated graph wider or narrower than the parent graph?

Graph is translated to the right 4 and up 6, and is narrower than the parent. New vertex is (4,6).

Graph the function f (x) = 4 abs(x). Now, consider the graph of g(x) = a abs(x). (Think outside the box on this one!) For what positive values of a will the graph of g(x) be wider than the graph of f (x)? How about narrower? Explain!

When 0 4, the graph of g(x) will be narrower than f (x).

Evaluate the function for the given value of x. f (3) = f (5) = f (6) =

f (3) = –1 f (5) = –3 f (6) = 18

Evaluate the function for the given value of x. f (0) = g (3) = h (–2) =

f (0) = 3 g (3) = 8 h (–2) = –5

Graph the piecewise function:

Graph the linear inequality: y ≤ 2x – 2

Graph the linear inequality: 5x – 7y < – 35

Graph the inequality: 7/3x > 7

Graph the inequality: y ≤ 2/3x – 2

A music store is holding a clearance sale. Their advertisement states that “all CDs are at least 25% off the regular price.” Write and graph an inequality that relates the sale price of a CD to the regular price.