Can someone help me with functions? (below)?

Question

If you can, please give me a detailed step by step of how to do this, and functions in general.

If f(4) = 0 and f(6) = 6, which of the following could represent f(x) ?
A. 2/3x – 4
B. x + 2
C. x – 4
D. 3/2x + 6
E. 3x – 12

Answer 1

You need to find a linear equation that fits the two points you have :(4, 0) and (6,6).
Use the slope-intercept form: y = mx + b.
Slope (m) is defined as the change in y over the change in x. Let (x1, y1) = (4,0) and (x2, y2) = (6,6). Then, m = (y2 - y1)/(x2 - x1)
m = (6 - 0)/(6 - 4) = 6/2 = 3

Now, use one of the points to find the intercept, b, using the m we just found. Let's use (x1, y1)
y1 = m(x1) + b
0 = 4(3) + b
0 = 12 + b
b = -12

Now, you've got the right equation. Just plug m and b into the generic formula:

y = 3x - 12

E is correct.

Answer 2

When you have a function f(4) = 0, this means that same as saying f(x) = 0, when x = 4. The same for f(6) = 6, is the same as f(x) = 6, when x = 6. The number in the brackets is what x equals.

So, plug in 4 for x in the possible equations and see if the answer comes out to be 0. For every equation that it does work, plug in 6 for x and see if the answer turns out to be 6. The one equation that works for both possible values of x is the right equation.

A. 2/3x - 4 = 2(4)/3 -4 = 8/3 - 4
This does NOT equal 0

B. x + 2 = 4 + 2 = 6
This does NOT equal 0

C. x - 4 = 4 - 4 = 0
This does equal 0. So check with 6:
C. x - 4 = 6 - 4 = 2
This does NOT equal 6

D. 3/2x + 6 = 3(4)/2 + 6 = 12/2 + 6 = 6 + 6 = 12
This does NOT equal 0

E. 3x - 12 = 3(4) - 12 = 12 - 12 = 0
Now check with 6:
E. 3x - 12 = 3(6) - 12 = 18 - 12 = 6

E. 3x - 12 checks out. This is the correct answer.

Answer 3

E. 3x-12
Because f(4) = 3(4) -12 = 0 and f(6) = 3(6)-12 = 6.
y = f(x) means y is a function of x. The value of y depends on x. So x is called the independent variable and y is the dependent variable.

If y=f(x) =x, then f(1) =1, f(2) =2, f(3) =3 , etc.
If f(x) = x^2+2x+1, then f(1)= 1^2 +2(1) +1 = 4.

The values that x can take on is called the Domain. The values that F(x) takes on is the range of the function.

Functions are characterized by having only one value of y for each value of x. If the same value of x generates two values of y that arethe same, then what you are dealing with is not a function. If you are looking at a graph, run a vertical line from left to right across the graph. If the vertical line cuts the graph in more than on place, then the graph is not a function. For example, if you are looking at the graph of a circle, when you move the vertical line from left to right , you would find that the vertical line would cutt the circle in two places. Hence a circlr is not a function.

Answer 4

PLug in the given values (4 and 6) to determine if they come out to the right results (0 and 6):

(A) (2/3)(4) - 4 = -4-3 => does not equal 0

(B) 4 + 2 = 6 => does not equal 0

(C) 4 - 4 = 0 => ok so far
6 - 4 = 2 => does not equal 6

(D) (3/2)(4) + 6 = 12 => does not equal 0

(E) 3(4) - 12 = 0 => ok so far
3(6) - 12 = 6 => ok

(E) is correct.

Answer 5

There's a few ways you could solve this (like with most things in math). What I would do is just plug in the numbers and see if they work.

if:
f(x)=3*x-12 then:
f(4)=3*4-12


Do you see how that works?

Does that equal 0?

How about f(6)? Does 3*6-12 equal 6?

This is good stuff to know, even though it doesn't seem so right now, it trains you in thinking logically, problem solving, creativity...yeah that's right, creativity.

Answer 6

that means that when x =4, f(x) = 0 and
when x = 6 f(x) = 6.

Plug it in.

3 * (6) - 12 = 6. thus, f(6) = 6.
3 * (4) -12 = 0 thus f(4) = 0.

Answer 7

The answer is E.

The way you solve this is as follows:

3(4) - 12 = 0

3(6) - 12 = 6

Answer 8

D