Question

mr. temples college algebra/precalculus exam

1. the graph below shows a piece - wise function. what is f(-2)?

a) 1
b) - 3
c) - 1
d) 3

1. a shipping company charges $5 for packages up to 2 lbs. which piecewise function models the cost c(x) for a package of weight x (lbs)?

a) c(x)=5 for x <= 2; c(x)=1.5(x - 2) for x > 2
b) c(x)=5x for x <= 2; c(x)=1.5x for x > 2
c) c(x)=5 + 1.5x for x > 2
d) c(x)=5+2x for x > 2

1. determine whether f(x)=x^4 - 3x^2 + 2 is odd, even, or neither.

a) odd
b) even
c) neither
d) both

1. from the graph below, which function is odd and which is even?

a) y = x^2 is even, y = x^3 is odd
b) y = x^2 is odd, y = x^3 is even
c) both are even
d) both are odd

Explanation:

21.

Step1: Locate x = - 2 on x - axis

Find the value of the function at x=-2 on the given piece - wise function graph.

Step2: Read the y - value

The y - value corresponding to x = - 2 on the graph is 3.

Step1: Analyze the base cost

The company charges $5 for packages up to 2 lbs, so for \(x\leq2\), \(C(x)=5\).

Step2: Analyze the cost for \(x > 2\)

For every pound over 2 lbs, it charges $1.50. The cost for LXI0 is the base cost of $5 plus $1.50 for each pound over 2. So \(C(x)=5 + 1.5(x - 2)\) for \(x>2\).

Step1: Recall the definitions

A function \(y = f(x)\) is even if \(f(-x)=f(x)\) and odd if \(f(-x)=-f(x)\).

Step2: Calculate \(f(-x)\)

Given \(f(x)=x^{4}-3x^{2}+2\), then \(f(-x)=(-x)^{4}-3(-x)^{2}+2=x^{4}-3x^{2}+2\).

Step3: Compare with \(f(x)\)

Since \(f(-x)=f(x)\), the function is even.

Answer:

D. 3

22.