Exercises on modular function

Learn modular function with solved and annotated exercises. Clear your doubts with the resolutions and get ready for the entrance exams and competitions.

question 1

Which of the following represents the graph of the function f(x) = |x + 1| - 1, defined as .

The)

B)

ç)

d)

and)

See Answer

Correct answer: e)

question 2

Write the formation law of the function f(x) = |x + 4| + 2, without module and in parts.

See Answer

For

f (x) = x + 4 + 2 = x + 6

For

f (x) = - x - 4 + 2 = - x - 2

Therefore

question 3

Plot the graph of the function f(x) = |x - 5| - 1, defined as , in the range [0, 6].

See Answer

The modular function |x - 5| -1, is formed, like the function |x|, by polygonal lines, that is, semi-straight lines with the same origin. The graph will be a horizontal translation to the right by five units and down by 1 unit.

question 4

The following graph represents the p(x) function. Plot the graph of the function q(x) such that q(x) = |p(x)|.

See Answer

Below, the p(x) function is represented in red and the q(x) function in blue dashes.

The graph of q(x) is symmetrical to that of p(x) with respect to the x-axis.

question 5

(Speck). Knowing that the graph below represents the real function f (x) = |x - 2| + |x + 3|, so the value of a + b + c is equal to

a) -7
b) -6
c) 4
d) 6
e) 10

See Answer

Correct answer: c) 4.

Idea 1: Rewriting modules by parts.

We have two points of interest, x = 2 and x = -3. These points divide the number line into three parts.

Idea 2: identifying a and b.

Thus a = -3 and b = 2

In this case the order does not matter as we want to determine a + b + c, and in an addition the order does not change the sum.

Idea 3: Identifying the sentence of the modules for x greater than or equal to -3 and less than 2.

For

Idea 4: determining c.

Doing f(x) to

Thus, c = 5.

Therefore, the sum value: a + b + c = -3 + 2 + 5 = 4

question 6

EEAR (2016). Let f(x) = |x - 3| a function. The sum of the values ​​of x for which the function takes the value 2 is

a) 3
b) 4
c) 6
d) 7

See Answer

Correct answer: c) 6.

Idea 1: Values ​​of x so that f (x) = 2.

We must determine the values ​​of x for which f(x) takes the value 2.

Writing the function in parts and without the module notation we have:

In equation I, making f(x) = 2

2 = x - 3
2 + 3 = x
5 = x

In equation II, making f(x) = 2 and substituting

2 = - x + 3
2 - 3 = -x
-1 = -x
1 = x

Idea 2: adding the values ​​of x that generated f (x) = 2.

5 + 1 = 6

Therefore, the sum of the values ​​of x for which the function takes the value 2 is 6.

question 7

esPCEx(2008). Looking at the graph below, which represents the real function f (x) = |x - k| - p, it can be concluded that the values ​​of k and p are, respectively,

a) 2 and 3
b) -3 and -1
c) -1 and 1
d) 1 and -2
e) -2 and 1

See Answer

Correct answer: letter e) -2 and 1

Resolution

k translates the function horizontally and is the abscissa of its vertex.

For , the function is shifted to the right.
For , the function is shifted to the left.

So, since the function vertex has abscissa -2, this is the value of k.

p translates the function vertically.

For , the function is shifted up.
For , the function is shifted down.

Therefore, p = -1.

learn more about modular function.

You may be interested in:

Occupation
quadratic function
linear function
polynomial function
exponential function
Math Formulas