# 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.

Q1:

Find the set of points of intersection of the graphs of and .

• A
• B
• C
• D

Q2:

Answer the following questions for the functions and .

Complete the table of values for .

 𝑥 −2 −1 0 1 2 𝑦
• A
• B
• C
• D
• E

Complete the table of values for .

 𝑥 −2 −1 0 1 2 𝑦
• 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:

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:

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:

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

Q10:

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,

Q16:

Find the -intercepts of the function .

• A2 and
• B2 and 7
• C and
• D and 7

Q17:

Find the set of points of intersection of the graphs of and .

• A
• B
• C
• D

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.

Q19:

Find the coordinates of the point at which the function intersects either the - or -axis.

• A
• B
• C
• D

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?