Section 2.1

Question 1

What type of mapping is a function and why? - one-to-one - one-to-many - many-to-one - many-to-many

Answer 1

one-to-one, many-to-one As for all x values, there is only one y value

Question 2

Give an example of a composite function, what does composite mean?

Answer 2

E.g. fg(x) or gf(x) Composite = to combine

Question 3

When finding the inverse function, what type of mapping must the original function be? - one-to-one - many-to-one Why can it not be the wrong answer?

Answer 3

One-to-one Because the inverse of many-to-one = one-to-many which is not a function

Question 4

When trying to find the inverse of a many-to-one function, what must you do?

Answer 4

Restrict the domain (x values) so that it becomes a one-to-one function

Question 5

When finding the range, what axis do you look for, what must you read carefully, and when the range could be any y-value, what do you write?

Answer 5

y-axis

Read the domain carefully in order to see if you write an inequality or simply the values

f(x) = R

Question 6

What is the modulus function, what is it also known as, what happens when:

f(x)>(=)0

f(x)<0

Answer 6

Non-negative numerical value

Absolute value

f(x)>(=)0, |f(x)| = f(x)

f(x)<0, |f(x)| = -f(x)

Question 7

How would you sketch:

• y = |3x-2|
• |2x-1| = 5

(Explain or write on board)

Answer 7

y = |3x-2|

Sketch 3x-2, then reflect line below x-axis into y-axis, so -2 would become 2 - all y-values in negative y-axis move to positive

|2x-1| = 5

Sketch |2x-1| and line y = 5

You can then solve the equation (there will be 2 solutions as the V will cross the line y = 5 twice)

Question 8

How would you solve the equations:

• |3x - 5| = 2 - 1/2(x)
• |5x - 1| > 3x

Answer 8

|3x - 5| = 2 - 1/2(x)

1. Sketch the graph (V and line)
2. Label intersections A and B
3. Solve for A: 3x - 5 = 2 - 1/2(x), x = 2
4. Solve for B: -(3x - 5) = 2 - 1/2(x), x = 6/5

|5x - 1| > 3x

1. Sketch graph (V and line)
2. Label intersections A and B
3. Solve for A: 5x - 1 = 3x, x = 1/2
4. Solve for B: -(5x - 1) = 3x, x = 1/8
5. Intersections: x = 1/2, x = 1/8

So solution to |5x - 1| > 3x, due to > means above line y = 3x,

So, x < 1/8, x > 1/2