Chapter 2.1, Problem 59E

Describe why the horizontal line test is an effective way to determine whether a function is one-to-one?

How do we determine the domain of a function defined by an equation?

Use the Vertical Line Test to determine whether the graph represents y as a function of x.

5. (a) Define piece-wise defined function. The function f is defined as -2 2 Find the domain and intercepts of f. Then graph it.

Choose the correct answer Please number of choose only please to all . 1-For what values of x is the function f(x)=-x2-2x+15  decreasing? A)(-infinity,-2].  B)(-infinity,-1)  C)[-2,infinity)  D)(-1, infinity) 2-For what values of x is the function f(x)=1/2x(x2-3x-9) decreasing? A)(-3,1) B) (-1, 3)      C)[-1, 3]  D)(-infinity,-1)union(3, infinity) 3-For what values of x is the function f(x)=4x2+4x-3  increasing? A)(-infinity,-1/2) B)(-infinity,-1/2]. C)(-1/2, infinity). D)[-1/2, infinity) 4-For what values of x is the function  F(x)=4x3+12x2-3  concave down ? A)(-infinity,-1) B)(-infinity,-2). C)(-1, infinity). D)(-2, infinity) 5-For what values of x is the function f(x)=4x3+12x2-3  concave up? A)(-infinity,-1) B)(-infinity,-2). C)(-1, infinity). D)(-2, infinity) 6- The critical values of f(x) = x+ 1/x is A) {0}  B) {1,-3}   C){1,-1}   D){2,-2})

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2x(x-4) (x+7)(3x-5) 5. Consider the function f(x)3D a) When does f(x)=0 ? b) When is f (x) undefined? c) Create a sign chart to determine when f(x)>0. d) Use the sign chart you created in part c to determine when f(x) < 0.

A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 inches.Write a list of six ordered pairs to show the height of the candle in inches (y) as a function of time in hours )x) from the first hour after it started burning. For example, the point (0,8) would represent a height of 8 inches after 0 hours. Explain how you obtained the ordered pairs Is this relation a function? Justify your answer using the list ordered pairs made in the first part. If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function and explain the answer using input and output values.

5. (a) Deline piece-wise defined function. The function fis defined as x + 3, -2 sx 2 Find the domain and intercepts of f. Then graph it.