# Worksheet: Intersection Points of Two Functions

In this worksheet, we will practice using a graphical or algebraic approach to solve systems of equations where one or both are nonlinear functions to find the intersection point of two functions.

**Q2: **

Answer the following questions for the functions and .

Complete the table of values for .

0 | 1 | 2 | |||

- A
- B
- C
- D
- E

Complete the table of values for .

0 | 1 | 2 | |||

- A
- B
- C
- D
- E

Use the tables of values to determine an intersection point of the two graphs.

- A
- B
- C
- D
- E

By extending the table up to , check if there are other intersection points. If so, find their coordinates.

- Ayes,
- Byes,
- Cyes,
- Dyes,
- Eno

**Q3: **

Answer the following questions.

Determine the equation of the line that passes through the points (2, 0) and (1, 2).

- A
- B
- C
- D
- E

Determine the equation of the line that passes through the points and .

- A
- B
- C
- D
- E

Hence, do the two lines intersect? If yes, state the point of intersection.

- AYes, they intersect at (2, 0).
- BYes, they intersect at (1, 2).
- CYes, they intersect at .
- DNo, they do not intersect.
- EYes, they intersect at .

**Q4: **

Answer the following questions.

Determine the equation of the line that passes through the points and .

- A
- B
- C
- D
- E

Determine the equation of the line that passes through the points and .

- A
- B
- C
- D
- E

Hence, do the two lines intersect? If yes, state the point of intersection.

- AYes, they intersect at .
- BYes, they intersect at .
- CNo, they do not intersect.
- DYes, they intersect at .
- EYes, they intersect at .

**Q5: **

Answer the following questions.

Determine the equation of the line that passes through the points and .

- A
- B
- C
- D
- E

Determine the equation of the line that passes through the points and .

- A
- B
- C
- D
- E

Hence, do the two lines intersect? If yes, state the point of intersection.

- AYes, they intersect at .
- BNo, they do not intersect.
- CYes, they intersect at .
- DYes, they intersect at .
- EYes, they intersect at .

**Q6: **

The given figure shows the graphs of the functions and . What are the points where ?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q7: **

The given figure shows the graphs of the functions and . What are the points where ?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q8: **

The given figure shows the graphs of the functions and . What are the points where ?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q9: **

The given figure shows the graphs of the functions and . What is the point where ?

- A
- B
- C
- D
- E

**Q11: **

The given diagram shows the graph of together with three lines of the form .

By solving , determine the coordinates of points and .

- A ,
- B ,
- C ,
- D ,
- E ,

Note that from , we know that line meets in the point , so is a factor of the cubic polynomial . Find the -coordinates of the other two intersections.

- A ,
- B ,
- C ,
- D ,
- E ,

Simplify the expression that states that the average rate of change of from to is to a quadratic equation in that has coefficients involving .

- A
- B
- C
- D
- E

The -coordinate of point is one where there is just one for which the average rate of change of is . By finding the discriminant of the quadratic expression find and .

- A ,
- B ,
- C ,
- D ,
- E ,

For what values of are there no points so that the average rate of change of from to is ?

- A or
- B or
- C or
- D or
- E or

**Q12: **

Find all values of where , given and .

- A or
- B or
- C or
- D or
- E or

**Q13: **

Find all the possible values of satisfying and given .

- A3 or 6
- B
- C
- D or

**Q14: **

The graphs of and intersect at the point , where and . Find the set of possible values of .

- A
- B
- C
- D

**Q15: **

The given figure shows the graphs of the functions and . What are the points where ?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q18: **

Use technology to plot the graphs of and . Find the coordinates where if the curves intersect, giving your answer to two decimal places.

- A ,
- B ,
- C ,
- D ,
- EThe curves do not intersect.

**Q20: **

Find the values of and given the function intersects the -axis at the point .

- A ,
- B ,
- C ,
- D ,

**Q21: **

If the function , where , and the function , where , find the solution set of which makes .

- A
- B
- C
- D

**Q22: **

What is the -coordinate of the point where the graphs of and intersect?