Comparing Functions

• The function f(x) has a greater y intercept than the function g(x)
• The function g(x) has a greater rate of change than the function f(x)
• The function g(x) has a greater y intercept than the function f(x)
• The rate of change for both g(x) and f(x) are equal 

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

• The rate of change of f(x) is less than the rate of change of g(x)
• The rate of change of f(x) is greater than the rate of change of g(x) 
• The y intercept of f(x) is equal to the rate of change of g(x) 
• The y intercept of f(x) is greater than the rate of change of g(x)

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

• Linear:  y = 2x - 5 
• Linear: y = -2x - 1
• Quadratic: y = (x - 2)²-5
• Exponential: y = 2(5)^x

• Linear: 2x - 2 
• Linear: 2x - 1 
• Quadratic: (x - 2)² + 4 
• Exponential: 2^x

• Linear: y = x + 6 
• Quadratic: (x - 1)² + 6
• Quadratic: (x - 2)² + 7
• Exponential: 6^x

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

• This is an example of exponential growth with the growth factor being 1.75.
• This is an example of exponential decay with the decay factor being .75. 
• This is an example of linear growth with the rate of change being .75.
• This is an example of linear decay with the rate of change being -.75. 

Tags

CCSS.HSF-IF.C.8B

• This is an example of exponential growth with the model being y = 3.5(1.20)^x
• This is an example of exponential decay with the model being y = 3.5(.20)^x
• This is an example of linear growth with the model being y = .20x + 3.50 
• This is an example of linear decay with the model being y = -.20x + 3.50 

Tags

CCSS.HSF-IF.C.8B

• f(x) because its rate of change is 4 while the rate of change for g(x) is 2 
• g(x) because  its rate of change is 4 while the rate of change for f(x) is 2
• g(x) because its graph appears steeper than that of f(x)
• Neither, both graphs appear to rise at the same rate 

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

• r(x) because its rate of change is 4 while the rate of change for s(x) is 2 over the interval [1,3]
• .  r(x) because its rate of change is 3 while the rate of change for s(x) is 2 over the interval [1,3]
• s(x) because its graph appears steeper than that of r(x) over the interval [1, 3]
• Neither, both graphs appear to rise at the same rate 

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

• Linear, because there is a constant rate of change
• Exponential, because there is a common ratio
• Quadratic, because there is a constant rate of change
• Quadratic, because the second difference is constant