Graphs of Lines with m=1

Order Id 910319
# 8
Given 𝑓(𝑥) = {𝑥 + 1,−2 < 𝑥 < 3
−𝑥, 𝑥 ≥ 3
Plot x+1 from point -2 to 3: x+1 is a straight line with m=1, and y-intercept =1
x -2 -1 0 1 2 3
f(x)=x+1 -1 0 1 2 3 4
Plot f(x)=-x from poin 3 to ∞: The graph is a straight line with m=-1 any y-intercept=0
x 3 4 10
f(x)=-x -3 -4 -10
#12

If 𝐻(𝑥) = √5𝑥2 − 3𝑥
3
𝐻(𝑥) = (𝑓 ∘ 𝑔)(𝑥), then 𝑓(𝑥) = √𝑥
3 𝑎𝑛𝑑 𝑔(𝑥) = 5𝑥2 − 3𝑥
#21-24 is done using the figure below
From the graph, 𝑦 =(𝑥 + 2)(𝑥 − 2) (𝑥
4) , from the figure, the following can be deduced:
#21: intervals is the function increasing
(−∞, −1.155) ∪ (1.155, ∞)
#22: intervals is the function decreasing
(−1.155, 1.155)
#23: local minimum of the function
(1.155, −0.77)
#24: local maximum of the function
(−1.155, 0.77)