# I need help w/ "If f(2) = -5 and f(-4) = 3, what is the value of f(9)?", ...

#### Wheaties

##### New member
I need help w/ "If f(2) = -5 and f(-4) = 3, what is the value of f(9)?", ...

How would i go about solving a problem like this?

If f(2) = -5 and f(-4) = 3, what is the value of f(9)? A) −41/4 B −83/4 C) −43/3
D) 43/3

and....

A local radio station sells program slots in 30-minute increments. The station is on the air Monday-Saturday from 6 AM to 10 PM. What is the maximum number of hours the station can sell? A) 112 B) 224 C) 96 D) 192

and finally...

If c/d =6, what is the value of 3d/c
A) 18 B) 1/2
C) 2 D) 1/18

#### mmm4444bot

##### Super Moderator
Staff member
How would i go about solving a problem like this?

If f(2) = -5 and f(-4) = 3, what is the value of f(9)?

A) −41/4 B −83/4 C) −43/3 D) 43/3
Here is just one approach. You could assume that function f is linear, and then use the Slope Formula to determine the line's slope. Once you know the slope, you could use the Point-Slope Formula, to get a definition for function f. Use the definition, to calculate f(9).

If these steps are not familiar to you, try checking some lessons and examples.

If the function notation y = f(x) is confusing, let us know.

A local radio station sells program slots in 30-minute increments. The station is on the air Monday-Saturday from 6 AM to 10 PM. What is the maximum number of hours the station can sell?

A) 112 B) 224 C) 96 D) 192
First, note that the question is about hours, not 1/2 hours, so you can ignore the first sentence.

Second, assume they want the maximum number of broadcast hours in a single Mon-Sat period.

If you switch to a 24-hr clock and ignore minutes (10PM=22, 6AM=06), you can use subtraction to calculate the number of hours the station is on the air each day. Multiply this daily total by the number of days in a single Mon-Sat period.

If c/d =6, what is the value of 3d/c

A) 18 B) 1/2 C) 2 D) 1/18
We can write Whole numbers (like 6) as a fraction: 6/1

c/d = 6/1

This shows that symbol c is 6 and symbol d is 1.

If we "flip" the fraction c/d, we get d/c.

(d/c is called the 'reciprocal' of c/d.)

c/d = 6/1

d/c = ?/?

Multiply d/c by 3. What do you get?

PS: In the future, please start a new thread for each exercise. :cool:

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#### HallsofIvy

##### Elite Member
How would i go about solving a problem like this?

If f(2) = -5 and f(-4) = 3, what is the value of f(9)? A) −41/4 B −83/4 C) −43/3
D) 43/3
If this is all you know, you can't. There are an infinite number of different functions that take on those values as x= 2 and x= -4. If, as mmm4444bot says, we assume[/b
a linear function, so that f(x)= ax+ b for some numbers, a and b, then f(2)= 2a+ b= -5 and f(-4)= -4a+ b= 3 so we have two equations to solve for a and b. Subtracting the second equation from the first, 6a= -8 so a= -4/3. Then 2a+ b= 2(-4/3)+ b= -8/3+ b= -5. b= 8/3- 15/3= -7/3. f(x)= (-4/3)x- 7/3.

and....

A local radio station sells program slots in 30-minute increments. The station is on the air Monday-Saturday from 6 AM to 10 PM.
There are 6 hours from 6 AM to noon and another 10 hours from noon to 10 PM so the statin is on the air for 16 hours Monday through Saturday. That is 6 days so the station is on the air 6*16 hours per week.

What is the maximum number of hours the station can sell? A) 112 B) 224 C) 96 D) 192

and finally...

If c/d =6, what is the value of 3d/c
A) 18 B) 1/2
C) 2 D) 1/18
c/d= 6= 6/1 so d/c= 1/6. Now multiply by 3.