Question

Which graph represents f(x)=

Answer 1

Answer:

Step-by-step explanation:

There are 3 graphs

Graph B:

f(x) = 9, -5<x<5

Symmetrical about x =0

To the right of x = 5, Passes through (5,9) and (15,30)

Use two point formula

y-9/(30-9) = x-5/(15-5)  or 21(x-5) = 10(y-9)

21(x-5) = 10(y-9)

because of symmetry about x =0, we get

equation as

f(x) = 2.1(x-5|)+90, for |x|>5

     =9, for |x|<5

Graph C is symmetric about x =-5

Hence the equation has an |x+5| in it

Because both sides straight line, right line passes through (-5,0) and (0,5) and hence right equation is x/-5 +y/5 =1

Or x-y = -5

Or y =x+5

Left side line is y = -x-5

Put together y = f(x) = |x+5| for graph C

iii) GraphD:

Graph D has 3 different lines.  Between 4 and t f(x) = 1

For x<4, Line passes through (3,3) and (4,1)

Using two point formula, y-3/(1-3) = x-3/(4-3)

Or -2x+6 = y-3 or 2x+y =9, for x <=4

For x>=4, line passes through (5,1) and (6,3)

Equation is (y-1)/(3-1) = (x-5)/(6-5) Or 2x-10 =y-1

2x-y =9

Together we can write f(x) as

y = |2x+9|,for x<=4 and x>=5

  = 1, for 4<x<5