1. Domain and range

2. Sketch a graph to help figure it out
Domain:
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
Range:
The range is the resulting y-values we get after substituting all the possible x-values
Sketch a graph to help figure it out
Range
Domain

3. Domain and range co-joined functions
Ten questions
Domain and range co-joined functions

4. State the range of this function
𝑓 𝑥 = 2𝑥−4 14−𝑥 ≤𝑥<6 6≤𝑥≤14
The function is the line between 2 and 6 and the 2nd straight line between 6 and 14
Range 0≤𝑦≤8
Domain 2≤𝑥≤14

5. State the range of this function
The function is the line between 0 and 2 and the 2nd straight line between 2 and 8
𝑓 𝑥 = 𝑥+4 4−𝑥 ≤𝑥<2 2≤𝑥≤8
Range 𝟎≤𝑦≤6
Domain 0≤𝑥≤8

6. State the range of this function
The function is the curve between -1 and 4
𝑓 𝑥 = 𝑥 2 −4𝑥 −1<𝑥≤4
Range −1<𝑦≤8
Domain −1<𝑥≤4

7. State the range of this function
The function is the curved graph between 0 and 3 and the straight line between 3 and 8
𝑓 𝑥 = 𝑥− ≤𝑥<3 3≤𝑥≤8
Range 2≤𝑦≤6
Domain 0≤𝑥≤8

8. Solve f(x) = 3 using a graph
5 of 10
Solve f(x) = 3 using a graph
𝑓 𝑥 = 𝑥 2 −2𝑥 −2≤𝑥<4 4≤ 𝑥≤8
The function is the curve between -2 and 4 and the straight line between 4 and 8
𝑓 𝑥 =3 at two
points on the graph
When 𝑥=−1
And 𝑥= 3
−1, 3
3, 3

9. 6 of 10
Define this function given by this graph
The function is the straight line between 0 and 3 and the curved graph between 3 and 7
𝑦=−𝑥 2 +8𝑥−11
Range −4≤𝑦≤5
Domain 0≤𝑥≤7
𝑓 𝑥 = 4 −𝑥 2 +8𝑥− ≤𝑥<3 3≤𝑥≤7

10. State the range of this function
The function is the curve between 2 and 7 and the 2nd curve between 7 and 11
𝑓 𝑥 = 6− (𝑥−5) 2 𝑥 2 −18𝑥 ≤𝑥<7 7≤𝑥≤11
Range −3≤𝑦≤6
Domain 2≤𝑥≤11

11. 𝑓 𝑥 = (𝑥+2) 2 +1 5− 1 2 𝑥 −1≤𝑥<3 3≤𝑥≤5
8 of 10
Define this function given by this graph
The function is the straight line between -1 and 3 and the curved graph between 3 and 5
(𝑥+2) 2 +1
5 − 1 2 𝑥
Range 0≤𝑦≤5
Domain −4≤𝑥≤10
𝑓 𝑥 = (𝑥+2) − 1 2 𝑥 −1≤𝑥<3 3≤𝑥≤5

12. State the range of this function
The function is the straight line between 0 and 3 and the curved graph between 3 and 7
𝑓 𝑥 = 4 −𝑥 2 +8𝑥− ≤𝑥<3 3≤𝑥≤7
Range 0≤𝑦≤6
Domain −4≤𝑥≤5

13. 10 of 10
Define this function given by this graph
The function is the straight line between -1 and 3 and the curved graph between 3 and 5
−𝑥 2 +6𝑥−3
Range −2≤𝑦≤6
Domain −1≤𝑥≤5
𝑓 𝑥 = 2𝑥 −𝑥 2 +6𝑥− −1≤𝑥<3 3≤𝑥≤5

14. One thing to improve is –
KUS objectives
BAT understand domain and range of functions
BAT define functions from graphs
self-assess
One thing learned is –
One thing to improve is –

15. END