Digital SAT Week 33

In the linear function f, f(0) = 8 and f(1) = 12. Which equation defines f?

• f(x) = 12x + 8

• f(x) = 4x

• f(x) = 4x + 12

• f(x) = 4x + 8

Answer explanation

Remember that f(0) = 8 means (0,8)

f(1) = 12 means (1,12)

So which equation will work for these 2 points?

Try f(x) = 12 + 8 8 = 12(1) + 8??? nope

Try f(x) = 4x + 12 8 = 4(0) + 12??? nope

Try f(x) = 4x 8 = 4(0) ??? nope

Try f(x) = 4x + 8 8 = 4(0) + 8 yep

12 = 4(1) + 8 yep

so f(x) = 4x + 8 is the equation created by these points

• If the width of the rectangle is 14 ft, then the area of the rectangle is 1,176 ft^2.

• If the width of the rectangle is 14 ft, then the length of the rectangle is 1,176 ft.

• If the width of the rectangle is 1,176 ft, then the length of the rectangle is 14 ft.

• If the width of the rectangle is 1,176 ft, then the area of the rectangle is 14 ft^2.

Answer explanation

The directions say the w represents the width and the answer is the area, so we are looking for statement that uses 14 and 1176 in the same way. 14 is the width and 1176 is the area

The circle shown has center O, circumference 144π, and diameters PR and QS. The length of arc PS is twice the length of arc PQ. What is the length of arc QR?

• 24π

• 48π

• 72π

• 96π

Answer explanation

since PR is a diameter it is cutting the circle into 2 halves each half circumference is 72pi

The semicircle QPS is made up of arc QP and arc PS

QP +PS = QPS = 72pi

PS = 2QP so

QP+ 2QP = 72pi

3QP = 72pi

QP = 24pi

QR and PS are the same size which is 2 QP so

2(24pi) = 48pi

A company that provides whale-watching tours takes groups of 21 people at a time. The company’s revenue is 80 dollars per adult and 60 dollars per child. If the company’s revenue for one group consisting of adults and children was 1,440 dollars, how many people in the group were children?

• 3

• 9

• 12

• 18

Answer explanation

there are going to be 21 people on the boat. so if there are 3 kids there will be 18 adults,

if there are 9 kids there will be 12 adults

if there are 12 kids there will be 18 adults,

if there are 18 kids there are 3 adults.

Also each kid is worth $60 and each adult is worth $80 and we know we got $1440

60C + 80A = 1440

now we need to test each case:

60(3) + 80(18) = 1440??? nope

60(9) + 80(12) = 1440??? nope

60(12) + 80(9) = 1440???? yep

so 12 kids and 9 adults

The function h is defined by h(x) = 4x + 28. The graph of y = h(x) in the xy-plane has an x-intercept at (a, 0) and a y-intercept at (0, b), where a and b are constants. What is the value of a + b?

• A) 21

• B) 28

• C) 32

• D) 35

Answer explanation

x intercept is where y = 0 and y intercept is where x = 0

0= 4x + 28

-28 = 4x

-7 = x (-7,0) for x intercept

y = 4(0) + 28

y = 0 + 28

y = 28 (0,28) for y intercept

so adding would be -7 + 28 = 21

Answer explanation

This is a good time for desmos

When you put this in you will see that the graph goes through the x axis three times (0, -8 and -13)

Now you have to understand that this makes the three factors

x (x+8) and (x + 13)

So the smallest POSITIVE will be at +8

Answer explanation

So this is a quadratic equation since we have x^2. If there is "one distinct real solution" then it only touches the x axis one time

Back in algebra 1 we learned that this makes the discriminant 0

discriminant is b^2 - 4ac. So let's solve that equation.

A = 1, B = 8 and C = a+1.5

0 = (8^2) - 4(1)(a+ 1.5)

0 = 64 - 4a - 6

0 = 58 - 4a

-58 = -4a

a = 14.5

• 
• 
• 
• 

Answer explanation

Notice that all of the tables have the same x values

Notice that each of these values makes one of the parentheses 0 . That would make f(x) =0 so we want the table where the y column is always (0 - 3) or (-3)

For the function q, the value of q(x) decreases by 45% for every increase in the value of x by 1. If q(0) = 14, which equation defines q?

Answer explanation

If it is DECREASING by .45 then we want an equation that will get smaller. That happens when the multiplier is less than 1. That happens for f(x) = .55 (14)^x and for f(x) = 14(.55)^x We can check by putting in the ordered pair of (0,14). An exponent of 0 makes the value equal to 1 so

F(0) = .55(1) nope

f(0) = 14(1) yep

The graph of y = f(x) + 14 is shown. Which equation defines function f?

• f(x) = -1/4 x - 12

• f(x) = -1/4 x + 16

• f(x) = -1/4 x + 2

• f(x) = 1/4 x - 14

Answer explanation

This is a negative slope so that rules out f(x) = 1/4x - 14.

The equation y = f(x) +14 says we took the original line and moved it up 14. To find the original lets move it back down 14.

The current line crosses the y axis at 2 so 2 -14 = -12

Putting that together we need f(x) = -1/4x - 12