Other Non-Linear Graphs

Other Non-Linear Graphs

Cubic and Exponential Graphs

Objectives

• Construct a table of values and draw the graph for cubic equation and simple sums of linear and non-linear terms;

• Construct a table of values and draw the graph of an exponential equations

• Interpret graph of higher order equations and use them to solve related equations

Cubic Graphs

• Open geogebra.org/calculator

• Draw these functions: y=x³, y=-x³, y=2x³, and y=1/2x²

• State the characteristics of the graphs!

Explore Cubic Graphs

• Draw y=x³, y=x³-3 and y=(x-2)³-3

• State the characteristics of the graphs!

​Cubic graphs characteristics

Subject | Subject

Some text here about the topic of discussion

In general, cubic graph is y = ax³, where a determines the direction and how wide the graph is.

​

The cube y = a(x-b)³​+c has:

• a value determines direction and how wide the graph is

• b value determines how many units the graph shifts to the right

• c value determi​nes how many units the graph shifts up and y-intercept

​

​

Multiple Choice

What is the y-intercept for y=x²-3 ?

• -3

• 3

• -2

Multiple Choice

Which graph has function y=-x³ ?

• red

• green

• blue

Multiple Choice

If the green graph represents y=x³, what does the blue graph represent?

• y=2x³

• y=-2x³

• y=1/2x³

Multiple Choice

If the red graph represents y=-x³, what does the green graph represent?

• y=(x-2)²+1

• y=(x+2)³-1

• y=(x+2)³+1

Multiple Choice

If the red graph represents y=-x³, what does the green graph represent?

• y=x³+3

• y=(x-3)³-1

• y=x³-3

Exponential graphs

• Using geogebra, draw y=2^x and y=2^-x

• Determine the x-intercept and y-intercept

• Draw y=2^x+3 and state the characteristics (asymptote, y-intercept)

​Exponential graphs characteristics

Subject | Subject

Some text here about the topic of discussion

In general, exponential graph is y = a^x, where a determines the direction and how wide the graph is.

​

The exponential y = a^x​+b has:

• a value determines direction and how wide the graph is

• y-intercept = b + 1

​

​

Graphs Summary

• We can determine the type of graph/curve by looking at the highest power

• The solution of the simultaneous equations is the intersection of the graphs (x-values)

Example 1

• The red graph is y=2^x and the green one is y=3-x

• The intersection of the curve and the line is the solution for 3-x=2^x

• The solution/root is x=1

Example 1

• The red graph is y=x and the purple one is y=x³

• The intersection of the curve and the line is the solution for x=x³

• The solution/root is x=-1, x=0, and x=1

• There are 3 intersection points, so there are 3 solutions/roots

Multiple Choice

What is the function of this graph?

• y=x

• y=x²

• y=x³

Multiple Choice

What is the function of this graph?

• y=2^x

• y=2^x-1

• y=2^x+1

Multiple Choice

What is the function of this graph?

• y=-x²

• y=x²-3

• y=-x²-3

Multiple Choice

How many solutions represented by the graphs?

• 1

• 2

• 3

Multiple Choice

How many solutions represented by the graphs?

• 1

• 2

• 3

Multiple Choice

How many solutions represented by the graphs?

• 1

• 2

• 3

Open Ended

Do you have any questions?