QUESTION 1The diagram below shows the functions of and𝑓(𝑥) =− 2𝑥2 + 5𝑥 + 3. is the turning point of and and are the𝑔(𝑥) = 2𝑥 + 1 𝐶 𝑓(𝑥), 𝐴 𝐸intercepts of . and are points on both graphs and . cuts𝑥 − 𝑓(𝑥) 𝐷 𝐴 𝑓(𝑥) 𝑔(𝑥) 𝑓(𝑥)the axis at and cuts the axis at .𝑦 − 𝐵 𝑔(𝑥) 𝑦 − 𝐼Figure 1: Diagram for Question 1.4Use the information and diagram above and:1.1 Calculate the length of:1.1.1 𝐴𝐸 (4)1.1.2 𝐵𝑂 (2)1.1.3 𝑂𝐹 (3)1.1.4 𝐶𝐹 (3)1.1.5 𝐵𝐼 (2)1.2 Determine the coordinates of .𝐷 (6)1.3 Write down the values of for which .𝑥 𝑓(𝑥) < 𝑔(𝑥) (2)1.4 Write down in the form using completing𝑓(𝑥) 𝑓(𝑥) = 𝑎(𝑥 − 𝑝)2 + 𝑞,the square. (4)1.5 Write down the domain of .𝑓(𝑥) (1)1.6 Write down the range of .𝑔(𝑥) (1)[28

Question 1. Graph each function, not by plotting points, but by starting with the graph of one of the standard functions?(Hint: First sketch the basic standard function and then show how it changes by shifting, compressing/stretching orreflection) (20 Point)a) 𝒚 = 𝟐|𝒙 + 𝟐| − 𝟏b) 𝐲 = √𝒙 − 𝟏𝟑 + 𝟏Question 2. Determine whether the graph of the functions below are symmetric about the y-axis, the origin, orneither?(20 Points)a) 𝒚 = 𝒙 − 𝒔𝒊𝒏𝒙b) 𝒚 = 𝒙𝟒 − 𝒙𝟐 − 𝟑Question 3. Find the following limits? (30 Points)a) 𝑙𝑖𝑚𝑥→44𝑥−𝑥22−√𝑥b) 𝑙𝑖𝑚𝑥→0tan 3𝑥sin 8𝑥c) 𝑙𝑖𝑚𝑥→∞9𝑥4+ 𝑥3𝑥4−5𝑥2+𝑥−2Question 4. Find Horizontal asymptotes of the Function below, and determine the behaviour of the function around theasymptotes?(30 Points)𝒇(𝒙) = 𝒙 + 𝟏𝒙𝟐 − 𝟏

QUESTION 4Given: and𝑓(𝑥) = 3𝑥−2 + 1 ℎ(𝑥) =− 1𝑥+524.1 Write down the equation of the asymptotes of 𝑓. (2)4.2 Determine the intercepts of𝑥 − 𝑓. (3)4.3 Determine the intercepts of𝑦 − 𝑓. (2)4.4 Sketch the graph of and on the same set of axes, clearly indicating𝑓 ℎthe distinctive features of the functions. (5)4.5 Determine the values for which𝑥 𝑓(𝑥) < ℎ(𝑥). (2)4.6 The line cuts at and . Write down the𝑦 =− 34 𝑥 + 254 𝑓 𝐸(3; 4) 𝐹coordinates of 𝐹. (7)

How does the graph of 𝑓(𝑥)=−32𝑥−4f(x)=−3 2x −4 differ from the graph of 𝑔(𝑥)=−32𝑥g(x)=−3 2x ?A.The graph of 𝑓(𝑥)f(x) is shifted four units to the right of the graph of 𝑔(𝑥)g(x).B.The graph of 𝑓(𝑥)f(x) is shifted four units down from the graph of 𝑔(𝑥)g(x).C.The graph of 𝑓(𝑥)f(x) is shifted four units up from the graph of 𝑔(𝑥)g(x).D.The graph of 𝑓(𝑥)f(x) is shifted four units to the left of the graph of 𝑔(𝑥)g(x).SUBMITarrow_backPREVIOUS

Use the figure to complete each part.F12GEH(a) Write two other names for ∠2.and(b) Name the sides of ∠GFE.and(c) Name the vertex of ∠1.

How is the graph of y=2x−1𝑦=2𝑥−1 transformed from y=2x𝑦=2𝑥?Horizontal shift Answer 1 Question 3 Answer 2 Question 3 unit(s).