Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for fraction bar(s)

f(x) {____if -1_< x _<1
____if 3_< x _<5

Answer 1

Answer: f(x) = 4 if -1 ≤x ≤ 1

f(x) = x - 1 if 3≤ x ≤ 5

Explanation:

if -1 ≤x ≤ 1

We can see that in this range the function is constant, f(x) = 4

if 3≤ x ≤ 5

In this region we can see a linear relationship, with the points (3, 2) and (5, 4)

as the extremes, we can find the slope of this linear equation as:

s = (4 - 2)/(5 - 3) = 2/2 = 1

So our equation is

f(x) = 1*x + b

to find the value of b we can evaluate our function in the first point, we know that when x = 3, y = 2, so we have:

2 = 1*3 + b

b = 2- 3 = -1

then f(x) = 1*x - 1

Then we have:

f(x) = 4 if -1 ≤x ≤ 1

f(x) = x - 1 if 3≤ x ≤ 5