KEY to Functions I: Overhead Sheets

You have been solving problems which involve “functions” and “functional relationships” for many years.

6th grade TAKS:

Which expression best represents the y values in terms of the x values?

x / 1 / 2 / 3 / 4 / 5 / 6
y / 2 / 5 / 8 / 11 / 14 / 17

A 1 – 3x

B x + 3

C 3x – 1 Answer: C

D 2x + 3

7th Grade TAKS:

Art’s department Store is having a sale. The table shows the regular price, r, and the sale price, s, of several items.

Sale Prices

Item / Regular Price
(r) / Sales Price
(s)
A / $5.00 / $2.50
B / $7.00 / $3.50
C / $10.00 / $5.00
D / $12.00 / $6.00

Which formula can be used to calculate the sale price?

A s = r – 2.5

B s = r x 2.0

C s = r x 0.5Answer: C

D s = r – 0.5

8th Grade TAKS:

The equation c = 0.75t represents c, the total cost of t tickets on a bus. Which table contains values that fit this equation? Answer: A

9th Grade TAKS:

Which equation could be used to generate this table of values?

x / y
-1 / 2
0 / 1
1 / 2
2 / 5

A y = -2x

B y = 2x + 1

C y = x + 1

D y = x2 + 1

Answer: D

10th Grade TAKS:

Which equation best describes the relationship between x and y in this table?

x / y
-4 / -11
-1 / -2
2 / 7
5 / 16

A y = ⅓x + 1

B y = ⅓x – 1

C y = 3x – 1

D y = 3x + 1 Answer: D

11th Grade TAKS:

Which equation best describes the relationship between x and y shown

in the table below?

x / y
1 / 3
2 / 12
4 / 48
6 / 108
9 / 243

A y = 3x

B x = 3y

C x = 3y2

D y = 3x2

Answer: D

11th Grade TAKS:

An equation can be used to find the total cost of buying square-foot floor tiles to cover an area of floor. Using the table below, find the equation that best represents y, the total cost, as a function of x, the number of square feet to be covered.

Number of Square Feet (x) / Total Cost (y)
1800 / $630
2300 / $805
2900 / $1015
Answer:G
F / x = 0.35y
G / y = 0.35x
H / x = 2.86y
J / y = 2.86x
Notes:

How do we recognize a function?

(Answers may vary) The graph of a function will pass the vertical line test.

The table of values representing points on the graph will not have the same independent value listed twice with a different dependent value, etc.

A function assigns exactly one value of the independent variable (oftenx) to the dependent variable (ofteny). In other words, the “x” value or independent variable cannot be listed more than once WITH A DIFFERENT Y VALUE.

Is this a function?

(1, 2), (-2, 7), (-1, 7), (8, -2)

yes

Is this a function? yes

Does this table of values represent a functional relationship?

Hours worked (h) / Salary (s)
2 / $10.00
3 / $15.00
4 / $20.00
2 / $25.00

no

Which of the following represents a function?

Answer: D

Know the difference between the independent and the dependent variable

Name the independent variable in this equation

y = 2x + 7 Answer: x

Name the independent variable in this table: Answer: x or Distance Stretched

For a car traveling at a speed of 50 miles per hour, the relationship between the distance traveled, d, and the time traveled, t, is described by the function

d = 50t. Which statement is true?

A The time traveled depends on the

distance traveled.

B The distance traveled depends on the

time traveled.

C The speed of the car depends on the

distance traveled.

D The speed of the car depends on the

time traveled.

Answer: B

On average, Jay can ride his bike 12 miles in one hour. The function m = 12h represents the number of miles, m, he can ride in h hours. Which quantity in this relationship is the dependent quantity?

A The number of miles he rides

B The number of hours he rides

C The miles per hour he rides

D Not Here Answer: A

In each equation below, name the dependent variable and the independent variable:

m = 2t – 16 dependent: m independent: t

y = 4x dependent: y independent: x

w = ½ v + 1 dependent: w independent: w

Zach is making an isosceles triangle to use as a model in math class. Its perimeter will be 24 inches. The equation

b = 24 – 2s describes b, the length of the triangle’s 3rd side, in terms of s, the length of each of its two congruent sides. What is the dependent variable in this equation?

A b

B s

C 24

D 2 Answer: A

Activity:

  • Think of a “memory technique” to remember that x is the independent variable. (Example: Malcolm X is an “independent” thinker)
  • Share your idea with another student.
  • Ask class to share the best ideas they.

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