Increase and decrease functions

In summary, the conversation discusses a graph that represents a function with variables. The question is how the graph will change when the variables are modified, specifically when the value of a is increased. The function is expected to increase, but the answer does not. The person is seeking an explanation for this.
  • #1
jose1
2
0
Hello
I have tried to resolve an exercise which is asking how the graph is modified according to the variables into the function. I would appreciate any help since accordin to my udnerstanding the function should increase

Please, follow below:
Suppose y0 is the y-coordinate of the point of intersection of the graphs below. Complete the statement below in order to correctly describe what happens to y0 if the value of a (in the blue graph of \(\displaystyle f(t)=a(1+r)t\) below) is increased, and all other quantities remain the same.

If the value of a change, the function should be increased, but the answer is not. I would like to understand why?

View attachment 8577Regards,

Jose
 

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  • #2
Let's examine a live graph:

[DESMOS]advanced: {"version":5,"graph":{"viewport":{"xmin":-5.365861436977749,"ymin":-1.3327205737064363,"xmax":17.212263563022272,"ymax":7.291467737981876}},"expressions":{"list":[{"type":"expression","id":"graph1","color":"#2d70b3","latex":"y=1.25^t","style":"SOLID"},{"type":"expression","id":"2","color":"#388c46","latex":"y=a\\cdot1.5^t","style":"SOLID"},{"type":"expression","id":"3","color":"#fa7e19","latex":"a=1","hidden":true,"sliderHardMin":true,"sliderHardMax":true,"sliderMin":"0","sliderMax":"5","sliderInterval":".01","style":"SOLID"}]}}[/DESMOS]

Move the slider, and look at how the intersection point changes when you change \(a\)...
 

FAQ: Increase and decrease functions

1. What is an increase function?

An increase function is a mathematical function where the output or dependent variable increases as the input or independent variable increases. In other words, as the value of the input increases, the value of the output also increases.

2. How is an increase function represented graphically?

An increase function is represented by a graph that slopes upwards from left to right. This is because as the input increases, the output also increases, creating a positive slope on the graph.

3. What is a decrease function?

A decrease function is a mathematical function where the output or dependent variable decreases as the input or independent variable increases. In other words, as the value of the input increases, the value of the output decreases.

4. How is a decrease function represented graphically?

A decrease function is represented by a graph that slopes downwards from left to right. This is because as the input increases, the output decreases, creating a negative slope on the graph.

5. How are increase and decrease functions related?

Increase and decrease functions are opposite of each other. While an increase function has a positive slope, a decrease function has a negative slope. They are both types of monotonic functions, meaning they either always increase or always decrease. They are commonly used in economics, statistics, and physics to model various real-life situations.

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