Module 2 Project 2 - MTH 161
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Northern Virginia Community College *
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161
Subject
Mathematics
Date
Feb 20, 2024
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docx
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Module 2 Project 2
MTH 161
Question 1: Problem 48, page 250
A.
Determine the vertex and interpret the meaning of (h,k) in the problem situation.
a.
(48,29.5) – This number represents how fast or slow the vehicle must go to have the optimal miles per gallon. X represents the speed of the vehicle, Whilst Y represents the Miles per gallon.
B.
Determine the x- and y- intercepts of the function. Interpret the meaning of each in the problem situation. Are all intercepts meaningful to the given problem? Explain.
a.
X-intercepts = {15.541,80.459}
b.
Y-intercepts = (0, -35.012) c.
All intercepts are meaningful in the equation. Even with the y-intercept being negative. If a vehicles engine is left running, even without the whole of the vehicle moving, the vehicle can still lose gas.
C.
Many real-world applications have a restricted domain and range. Determine an appropriate domain and range for the problem you chose. a.
Domain: 0<x<81
b.
Range: -36<0<30
Question 2:
A.
Include a screenshot of the graphs with coordinate points of the x-intercepts and intersection points labeled.
a.
b.
X-intercepts of:
i.
5x
3
-4x
2
-7x+5 = {-1.157, 0.673, 1.283}
ii.
-x
4
+4 = {-1.414, 1.414}
B.
Solve for the following inequalities using interval notation
a.
F(x) > g(x)
i.
-1<x<0.134
ii.
X>1.356
b.
F(x) < 0 i.
X<-1.157
ii.
0.673<x<1.284
Question 3: Create
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A. Zeros
a.
(-3.5,0)
B.
Equations of asymptotes
a.
X= -3
b.
Y= 2
C.
The coordinates of any holes
a.
(-2,3), (-4,1)
D. Y-intercepts
a.
(0,2.333)
E.
End behavior. fill in the blanks:
a.
As 𝑥
→ ∞, 𝑦
→ __2__ and 𝑥
→ −∞, 𝑦
→ __2___.