 # The Analysis of a Function

## Question

1. Consider the function f(x)=4x²-8x+3 or f(x)=4x²-8x+3
A. Determine the graph opens up or down. Explain answer.
B. Determine the vertex of the graph of the quadratic function.
C. Determine the axis of symmetry of the graph of the quadratic function.
D. Determine intercepts if any of the graph of the quadratic function.
E. Use the information from parts (a)-(d) to graph the quadratic function.
F. Based on the graph, determine the domain and the range of the quadratic function.
G. Based on the graph, determine where the function is increasing or decreasing.

2. The monthly cost of renting a compact car is \$139.50 plus \$0.20 per mile.
A. find a linear function that express the cost C as a function of miles driven m.
B. What is the rental cost if 920 miles are driven?
C. How many miles are driven if the rental cost is \$312.10

3. The value of a car can be modeled by the linear function V(x)=-4000x+48000 where x is the number of years since 2008.
A. Find the value of the car in 2010.
B. Find the value of the car in 2012.
C. When will the car be worth 20,000?
D. Give and interpret the slope and the y-intercept of the graph of function.
E. Give the domain and the range of the graph of the function.

4.    The price p( in dollars) and the quantity x sold of a certain commodity obey the demand equation p=(-1/5)x+80
A. Find a model that expresses the revenue R as a function of x.
B. What is the domain of R?
C. What is the revenue if 150 units are sold?
D. What quantity x maximizes the revenue? What is the maximum revenue?
E. What price should the company charge to maximize revenue?

5.   Martha has 240 feet of fence available to enclosed a rectangular field.
A. Express the area A of the rectangular field as a function x, where x is the length of the rectangular field.
B. For what value of x is the area largest?
C. What is the maximum area?

6. Determine whether f(x)=-3x²+12x+11 has a minimum or maximum value. Then find the minimum or maximum value.

7. Solve x²-6x+8>0 or x²-6x+8>0

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