Question

f(x) = x
f(x) = x^2
f(x) = 2^x
1) Which functions intersect?

2) How many points of intersection are there?

3) What does a point of intersection mean?

Answer 1

Answer:

Part 1) In the procedure

Part 2) There are 4 points of intersection (see the procedure)

Part 3) The answer in the procedure

Step-by-step explanation:

we have

$f(x)=x$ -----> linear function

$f(x)=x^{2}$ ----> quadratic function

$f(x)=2^{x}$ ----> exponential function

Part 1) Which functions intersect?

using a graphing tool

we have that

$f(x)=x$ intersect with $f(x)=x^{2}$

$f(x)=x^{2}$ intersect with $f(x)=x$ and $f(x)=2^{x}$

$f(x)=2^{x}$ intersect with $f(x)=x^{2}$

see the attached figure

Part 2) How many points of intersection are there?

In total there are 4 points of intersection

so

Between

$f(x)=x$ and $f(x)=x^{2}$

there are 2 points -----> (0,0) and (1,1)

Between

$f(x)=2^{x}$ and $f(x)=x^{2}$

there are 2 points -----> (-0.77,0.59) and (2,4)

Part 3) What does a point of intersection mean?

we know that

A point of intersection between two functions means a common solution for both functions.

so

Example 1

The point (0,0) is a point of intersection between $f(x)=x$ and $f(x)=x^{2}$

For x=0

Find the value of both functions

$f(x)=x$ -----> $f(0)=0$

$f(x)=x^{2}$ ----> $f(0)=0^{2}=0$

Both functions have the same value

Example 2

The point (2,4) is a point of intersection between $f(x)=2^{x}$ and $f(x)=x^{2}$

For x=2

Find the value of both functions

$f(x)=2^{x}$ -----> $f(2)=2^{2}=4$

$f(x)=x^{2}$ ----> $f(2)=2^{2}=4$

Both functions have the same value