Question

The table represents a linear function. x and f(x) −2,−2 and -1,1 and 0,4 and 2,10 and 4,16 What is the value of the function when x=−3?

(A) -13 (B) -9 (C) -5 (D) 9

Answer 1

it should be C if not get back with me

Answer 2

The value of f(-3) will be y=-5. (option C)

Explanation:

To find the value of f(3) we could first state the expression for f(x). The expression for y=f(x) can be determined by the following formula:

y-yo=m(x-xo)

The values of xo and yo are the coordinates of whichever of the known point, and m is the slope of linear function:

m=(y1-yo)/(x1-xo)

There y1, x1 is the coordintes of a different point. Choosing the points like:

(xo,yo)=(-2,-2)

(x1,y1)=(4,16)

The value of m results:

m=[16-(-2)]/[4-(-2)] = [18/6] = 3

Then by replacing m and (xo,yo) in the equation of y:

y-(-2)=3(x-(-2))

y+2=3(x+2)

f(x)=y=3x+6-2

f(x)=y=3x+4

Finally we replace the value of x=-3:

f(-3)=y=3(-3)+4

f(-3)=y=-9+4=-5