ISAT Target E | Define, evaluate, and compare functions (part 1)

Which relations defines y as a function of x?

• y = 2.4x

• 
• 

Answer explanation

The equation y = 2.4x has one y value for every x value.

The table has 2 y values for x = 4 meaning it is not a function.

The inequality graph has multiple y values for every x value.

Functions do not have exponents (other than 1) on the y variable.

Which equation defines p as a function of t?

• p = 3t + 2

• t = 3p + 2

• p = 0t + 2

• t = 0p + 2

Answer explanation

To describe p as a function of t, p must be the dependent variable.

p = 3t + 2 | as t changes, p will change

t = 3p + 2 | as p changes, t will change

p = 0t + 2 | this one is p = 2, it does not matter what t is

t = 0p + 2 | this on is t = 2, it does not matter what t is

p = 3t + 2 is the answer

Select all ordered pairs that correspond to (input, output) pairs for the function

y = —6x + 7

• (1, 1)

• (–1, 1)

• (–6, 7)

• (3, –11)

Answer explanation

Solutions for y = —6x + 7

(1, 1) | 1 ? -6(1) + 7 ? 1 = -6 + 7 | 1 = 1 | Yes

(–1, 1) | 1 ? (-6)(-1) + 7 ? 6 + 7 |

1 = 13 | No

(–6, 7) | 7 ? (-6)(-6) + 7 ? 36 + 7 | 7 = 43 | No

(3, –11) | -11 ? (-6)(3) + 7 ? -18 + 7 | -11 = -11 | Yes

A swimming pool had 30 gallons of water in it. Then water was added to the pool at a rate of 5 gallons per second.

The function y = 5t + 30 describes the relationship between the number of gallons, y, and the number of seconds water was added, t.

• (45, 3)

• (3, 45)

• (0, 30)

• (30, 0)

Answer explanation

y = 5t + 30

(45, 3) | 3 ? 5(45) + 30 ? 225 + 30 | 3 = 255 | No

(3, 45) | 45 ? 5(3) + 30 ? 15 + 30 | 45 = 45 | Yes

(0, 30) | 30 ? 5(0) + 30 ? 0 + 30 ? | 30 = 30 | yes

(30, 0) | 0 ? 5(30) + 30 ? 150 + 30 | 0 = 180 | no

Which function could have produced the values in the table?

• y = –x ─ 14

• y = -3x + 2

• y = 3x ─ 22

• y = 3x + 2

Answer explanation

The equation that works for all pairs in the table is

y = 3x + 2

-10 = 3(-4) + 2 | -10 = -12 + 2

-7 = 3(-3) + 2 | -7 = -9 + 2

-4 = 3(-2) + 2 | -4 = -6 + 2

-1 = 3(-1) + 2 | -1 = -3 + 1

2 = 3(0) + 2 | 2 = 0 + 2

Make sure you test each of the values of the table. When you come across a false statement, you know that can't be the equation.

A swimming pool has 30 gallons of water in it. Water is added to the pool at a rate of 5 gallons per second.

Which equation models the relationship between W, the number of gallons of water, and t, the number of seconds water is being added to the swimming pool?

• W = 30t + 5

• W = 5t + 30

• W = t + 35

• W = 35t

Answer explanation

A swimming pool has 30 gallons of water in it. | The pool starts with 30 gallons. So at 0 seconds the pool has 30 gallons. The y-intercept is 30.

Water is added to the pool at a rate of 5 gallons per second. | The rate is 5 gallons per second which is also the slope (or m in y = mx + b or in this case W = mt + b).

The equation is W = 5t + 30

Which of the following functions has the greatest rate of change?

• y = 3x – 1

• 
• 

• could be linear
• is not linear

Answer explanation

A linear function creates a straight line. This function will create a straight line.

The graph shows a line that​ (a)  

• is not linear
• could be linear

Answer explanation

A liner function creates a line that is straight. This line is not straight, therefore this line does not represent a linear function.

The table represents a line that​ (a)  

• could be linear
• is not linear

Answer explanation

The x values are changing by + 1 each time; The y values are changing by +4 each time.

The rate of change is constant with the data that is given, therefore this table represents a line that could be linear. Since it is not a complete set of data we don't know for sure, but there is nothing to indicate that it is not linear.