Unit 9, Lesson 12
Reasoning about Exponential Graphs (Part 1)
Integrated Math 1
Practice
Problem 1
Here are equations defining three exponential functions \(f\), \(g\), and \(h\).
\(f(x) = 100 \boldcdot 3^x\)
\(g(x) = 100 \boldcdot (3.5)^x\)
\(h(x) = 100 \boldcdot 4^x\)
- Which of these functions grows the least quickly? Which one grows the most quickly? Explain how you know.
-
The three given graphs represent \(f\), \(g\), and \(h\). Which graph corresponds to each function?
Graph of three increasing exponential functions, xy-plane, origin O. Horizontal axis, scale 0 to 3, by 1’s. Vertical axis, scale 0 to 6,000, by 1,000’s. Function C is red and has these points: (0 comma 100), (1 comma 300), (2 comma 900) and (3 comma 2,700). Function A is blue and has these points: (0 comma 100), (1 comma 400), (2 comma 1600) and (3 comma 6,400). Function B is green and has these points: (0 comma 100), (1 comma 350), (2 comma 1,225) and (3 comma 4,287 point 5. - Why do all three graphs share the same intersection point with the vertical axis?