Precalculus Exam 2 Fall 2023 PDF

## Math.1210.101A Management Precalculus EXAM 2 Fall 2023 **Instructions:** SHOW ALL YOUR WORK. Answers with no supporting steps leading to a correct result will receive no credit. It is assumed that you will ONLY USE the given formula sheet. You have up to 75 minutes to work on the exam. Put away...

## Math.1210.101A Management Precalculus EXAM 2 Fall 2023 **Instructions:** SHOW ALL YOUR WORK. Answers with no supporting steps leading to a correct result will receive no credit. It is assumed that you will ONLY USE the given formula sheet. You have up to 75 minutes to work on the exam. Put away your phone. If I see you looking at one, you will immediately get a 0 for the exam score. If I cannot read your work, I will not grade it. If you do not print your name, you will lose 5 points. Simplify all answers as much as possible. ### 1. Solve the for *x*: **a)** *x*²-12*x*+32=0 (use factoring) Formula)=0 **bi)** *x*²+4*x*=-2 (use quadratic ### 2. Given the following revenue and cost functions, form the profit function. Find the maximum profit. How many units must be sold to have maximum profit? *R(x)=-0.25*x*²+280*x* *C(x)=80*x*+10,000* ### 3. Solve for *x*: **a)** 2*x*-4-2=160 **b)** 3*x*-9 / 4 = 5 ### 4. The table below gives the millions of U.S. citizens with cancer from 2020 and projected to 2024. Find a quadratic function that models this data where *x* equals the number of years after 2020 and *y* equals the number of millions of American with cancer (round your numbers to three decimal places). In what year after 2020 does the model predict that 1.1 million of Americans will have cancer? Solve it graphically on your calculator. Year | number ------- | -------- 2020 | 1.3 2021 | 2.1 2022 | 2.9 2023 | 2.3 2024 | 1.8 ### 5. Use the properties of exponents to simplify the expression, the result should not have a negative exponent. **a)** (2 *x*-1/2 *y*4/3) (8*x*3/2 *y*2/3) **b)** (4*a*³ *b*² / -5*a*²*b*) ^ -2 ### 6. Use the functions *f(x)=8x²+x* and *g(x)=-2x+12* to find the following: **ai)** (*f*+*g*)(*x*) **bi)** (*f*-*g*)(*x*) **ci)** (*f*o*g*)(2)=*f*(*g*(2)) **di)** *f'(-2) / g* ### 7. Determine the parent function and describe the sequences of transformation used to obtain the given function graph both parent function and the transformed one below. *y=-(x+3)²+1* The graph is a parabola opening downward, with the vertex at (-3,1). The parent function is *y=x²*, which has been shifted 3 units to the left and 1 unit up. The function has also been reflected across the *x*-axis. ### 8. Is the function *f(x)=x5+3a* a one-to-one function? Explain. Does it have inverse? If does, find the inverse function algebraically. Graph both functions. *f(x)= x⁵ + 3 is a one-to-one function because it passes the horizontal line test. This means that no horizontal line intersects the graph of the function more than once. Therefore, the function has an inverse. To find the inverse function, we can follow these steps: 1. Replace *f(x)* with *y*. 2. Swap *x* and *y*. 3. Solve for *y*. 4. Replace *y* with *f⁻¹(x)*. This gives us the inverse function: *f⁻¹(x)= (x-3) ^ 1/5* The graph of the function and its inverse are symmetrical about the line *y=x*. ### 9. (Extra Credit 5 points.) Is *f(x)* an even function, odd function, or neither? Justify your answer. *f(x)= (3*x*²+8*x*) / *x*²* An even function has the property that *f(-x) = f(x)* for all *x* in the domain. An odd function has the property that *f(-x) = -f(x)* for all *x* in the domain. Let's check if *f(x)* satisfies either of these properties: *f(-x) = (3(-x)² + 8(-x)) / (-x)² = (3x² - 8x) / x²* Since *f(-x) ≠ f(x)* and *f(-x) ≠ -f(x)*, the function is neither even nor odd.