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

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

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

The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does not exist, enter DNE.)The x y coordinate plane is given. There is one curve and one point on the graph. The point occurs at (−1, 3). The curve enters the window at (−2, −1), goes up and right, passes through the open point (−1, 1), changes direction at (0, 2), goes down and right, and passes through the open point (2, −1). At this point, the curve turns sharply forming a cusp, goes up and right, and exits the window at (4, 2). The x y coordinate plane is given. There are two curves on the graph. The first curve enters the window at (−2, 0), goes up and right, and ends at the closed point (0, 3). The second curve begins at the open point (0, 1), goes up and right, and passes through (2, 2). At this point, the curve turns sharply forming a cusp, goes down and right traveling in a straight line, and exits the window at (4, −2).(a)lim x→2 [f(x) + g(x)](b)lim x→0 [f(x) − g(x)](c)lim x→−1 [f(x)g(x)](d)lim x→3 f(x)g(x)(e)lim x→2 [x2f(x)](f)f(−1) + lim x→−1 g(x)

Instructions: Determine whether graphs of each of the exponential functions would show vertical stretch or vertical compression and whether there is reflection over the x𝑥-axis.y=−2(3)x𝑦=−2(3)𝑥Vertical Answer 1 Question 14Reflection over the x𝑥-axis? Answer 2 Question 14

For the function f whose graph is shown, state the following. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.)FigureThe x y coordinate plane is given. Refer to the adjacent description for more details.Description(a)lim x → −7 f(x)(0,2) (b)lim x → −3 f(x)DNE (c)lim x → 0 f(x)2 (d)lim x → 6− f(x)∞ (e)lim x → 6+ f(x)−∞ (f)the equations of the vertical asymptotes (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)x = (−3,6)