Download 3.4 Graphing Functions Graph, find the domain, range, and any

3.4 Graphing Functions
Graph, find the domain, range, and any points of discontinuity
𝑥 + 1, 𝑖𝑓 𝑥 ≤ 1
1) 𝑓(𝑥) = {1
𝑥 + 3, 𝑖𝑓 𝑥 > 1
2
Domain:
Range:
Points of Discontinuity
3𝑥,
𝑖𝑓 𝑥 ≤ −2
1
2) 𝑓(𝑥) = {2 𝑥 − 1, 𝑖𝑓 − 2 < 𝑥 < 3
𝑥 − 3,
𝑖𝑓 𝑥 ≥ 3
Domain:
Range:
Points of Discontinuity
3) 𝑓(𝑥) = {
2𝑥 + 1, 𝑖𝑓 𝑥 > −2
3,
𝑖𝑓 𝑥 ≤ −2
Domain:
Range:
Points of Discontinuity:
4) Given f(x)= 3x2 + x – 3
Find Vertex__________
Is it max or min?___________
What is the max or min value?________
Axis of Symmetry_______ x-intercept(s)_______________ y-intercept(s)_____________
Intervals of increasing behavior____________
decreasing behavior________________
Domain________________
Range________________________
3.5 Combining Functions
5) Given: f(x)= x2 - 5x
g(x)= 9x + 4
f+g
Perform the indicated operation and state its domain.
f-g
fg
f/g
f૦ g
g૦ f
6) Find the domain of g(x) =√𝑥 2 + 4𝑥 − 32
7) Find the x- and y- intercepts of f(x) = x2 + 10x - 56
3.6 Inverse Functions
Determine whether the function is one-one.
8)______
Write the inverse of each function.
2𝑥
9) 𝑓(𝑥) =
3𝑥+1
10) 𝑓(𝑥) = 2√𝑥 + 9
11. Find domain and range from graph
D:
R:
12. Find domain and range from this equation
𝑓(𝑥) = 3x2 + x
D:
R:
13. Draw the graph and state domain, range, intercepts, inc/dec. behavior, and any discontinuity for
this function 𝑓(𝑥) = 𝑥 2 − 8𝑥 + 4
D:
R:
x-int:
y-int:
Inc:
Dec:
Disc:
14. Write the piecewise function of this graph.
𝑓(𝑥) =
15. Find a linear function f(x) given f(-2) = 5 and f(3) = 7.
16. Combining functions and their domains
a. If f(x) = 2x + 5 and g(x) = 3x – 2, find f – g and state the domain
b. If f(x) = 9x – 3 and g(x) = 3x + 3, find
𝑓(𝑥)
𝑔(𝑥)
and state the domain
c. If f(x) = x2 – 5x + 6 and g(x) = x2 – 4, find (f)(g) and state the domain
17. Let f(x) = 4x – 8 and g(x) = 2x + 1. Find (f o g)(4)
18. Find the inverse of f(x) = x2 – 5, x ≥ 0