Lesson Worksheet: Intersection Points of Two Functions Mathematics
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
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,
Q17:
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:
If the function , where , and the function , where , find the solution set of which makes .
- A
- B
- C
- D
Q21:
What is the of the point where the graphs of and intersect?
Q22:
Use technology to plot the graphs of and . Find the coordinates where if the curves intersect, giving your answer to two decimal places.
- AThey intersect at and .
- BThe curves do not intersect.
- CThe curves are the same, so intersect everywhere.
- DThey intersect at .
- EThey intersect at .
Q23:
The given figure shows the graphs of the functions and . What is the point where ?
- A
- B
- C
- D
- E