Algebra 1 | Unit 5 | Lesson 19: Which One Changes Faster? | Practice Problems

Functions \(a,b,c,d,e,\) and \(f\) are given below. Classify each function as linear, exponential, or neither.

• a(x)=3x

• b(x)=3^x

• e(x)=9\cdot3^x

• d(x)=9+3x

• c(x)=x^3

Here are 4 equations defining 4 different functions, \(a, b, c,\) and \(d\). List them in order of increasing rate of change. That is, start with the one that grows the slowest and end with the one that grows the quickest.

• a(x)=5x+3

• b(x)=3x+5

• c(x)=x+4

• d(x)=1+4x

Functions \(m\) and \(n\) are given by \(m(x)=(1.05)^x\) and \(n(x)=\frac{5}{8} x\). As \(x\) increases from 0: Which function reaches 30 first?

• m

• n

Functions \(m\) and \(n\) are given by \(m(x)=(1.05)^x\) and \(n(x)=\frac{5}{8} x\). As \(x\) increases from 0: Which function reaches 100 first?

• m

• n

The functions \(f\) and \(g\) are defined by \(f(x) = 8x + 33\) and \(g(x) = 2 \cdot (1.2)^x\). Explain why the graphs of \(f\) and \(g\) meet for a positive value of \(x\).

A couple needs to get a loan of $5,000 and has to choose between three options. Option A: \(2\frac{1}{4}\%\) applied quarterly Option B: \(3\%\) applied every 4 months Option C: \(4\frac{1}{2}\%\) applied semi-annually If they make no payments for 5 years, which option will give them the least amount owed after 5 years? Use a mathematical model for each option to explain your choice.

• Option A

• Option B

• Option C

Here are graphs of five absolute value functions. Match the graph and equation that represent the same function.

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