Question

What does f mean in f(x)=3/2x+2? Also do the two points 0,2 and 2,5 work with the equation?

Answer 1

Answer:

(0, 2) and (2, 5) are solutions to the function.

Step-by-step explanation:

Given the following linear function:

$\displaystyle\mathsf{f(x)\:=\:\frac{3}{2}x\:+\:2 }$

"f(x)" is a function notation.  

"f" represents the function name. In function notations, you can use any letter to represent a function name. However, "f" is commonly used to express function notations.

"x" is your input variable. This is the x-values that you substitute into the function to get an output, or y-value.

f(x) is your output value.

We are also given the following points:  (0, 2) and (2, 5).

In order to determine whether these points work with the given function, simply substitute their values into the function.

(0, 2) where x = 0, y = 2:

$\displaystyle\mathsf{f(x)\:=\:\frac{3}{2}x\:+\:2 }$

$\displaystyle\mathsf{f(0)\:=\:\frac{3}{2}(0)\:+\:2 }$  ⇒ The function notation, "f(0)" simply means the function of zero, which corresponds to the input value of zero (0).

Next, substitute the value of y = 2 into the function as an output value:

$\displaystyle\mathsf{2\:=\:\frac{3}{2}(0)\:+\:2 }$

2 = 0 + 2

2 = 2 (True statement).  This means that the point, (0, 2), is a solution to the given function. The point (0, 2) represent the given function's y-intercept, which is the point on the graph where it crosses the y-axis.  The y-coordinate of 2 is the value of b in the slope-intercept form, y = mx + b.

(2, 5) where x = 2, y = 5:

We will do the same process for (2, 5):

$\displaystyle\mathsf{f(x)\:=\:\frac{3}{2}x\:+\:2 }$

$\displaystyle\mathsf{f(2)\:=\:\frac{3}{2}(2)\:+\:2 }$

Substitute the value of y = 5 into the function as an output value:

$\displaystyle\mathsf{5\:=\:\frac{3}{2}(2)\:+\:2 }$

5 = 3 + 2

5 = 5 (True statement).  This means that the point, (2, 5), is also a solution to the given function.

Answer 2

Answer:

f(x) means y

Points 0,2 and 2,5 work with the equation

Step-by-step explanation:

f(x) means y

For 0, 2

y = 3/2(0) + 2

y = 2

For 2,5

y =3/2(2) + 2

y = 5