Linear vs Exponential

Which statement below is TRUE regarding the two functions?

• Both functions are linear

• Both functions are increasing

• Both functions have a y-intercept of 1

• Both functions are exponential growth

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Which statement below is TRUE regarding the functions pictured?

• Both functions have a y-intercept of 3

• Both functions are increasing

• Both functions are linear

• Both functions have a MULTIPLYING pattern

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

True or False: All increasing exponential functions eventually exceed all increasing linear functions.

• True

• False

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

Which statement compares the graphs of f(x) and g(x) over the interval [0, 5]?

• The graph of f(x) always exceeds the graph of g(x) over the interval [0, 5].

• The graph of g(x) always exceeds the graph of f(x) over the interval [0, 5].

• The graph of g(x) exceeds the graph of f(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of f(x) exceeds the graph of g(x).

• The graph of f(x) exceeds the graph of g(x) over the interval [0, 4], the graphs intersect at a point between 4 and 5, and then the graph of g(x) exceeds the graph of f(x).

• The exponential function NEVER exceeds the linear Functions

• The exponential functions ALWAYS exceeds the linear function

• The linear function exceeds the exponential function over the interval [0, 4]

• The exponential function exceeds the Linear functions over the interval [3, 4]

• The exponential function exceeds the Linear functions over the interval [4, 5]

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.3

Challenge 2:
Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x). 

• g(x) rate of change is ALWAYS greater than f(x) rate of change. 
• g(x) is NEVER greater than f(x) rate of change. 
• g(x) will eventually exceed the rate of change of f(x). 
• There is not enough information to compare the rate of change of f(x) to g(x). 

Tags

CCSS.8.F.A.2

CCSS.HSF.IF.C.9

The image shows the graphs of a linear function, f(x), exponential function, g(x), and quadratic function, h(x).

Over what positive interval does f(x) exceed g(x)?

• (0,6)

• (0,5.5)

• (6,∞)

• (-∞,6)

The image shows the graphs of a linear function, f(x), exponential function, g(x), and quadratic function, h(x).

Using only what can be seen in the image, for what positive values does g(x) exceed h(x)?

• (0,1)

• (1,0)

• (1,∞)

• (1,6)

• Exponential Functions NEVER exceed Linear Functions

• Exponential Functions ALWAYS exceed Linear Functions

• The linear function exceeds the exponential function over the interval [0, 6]

• The exponential function exceeds the Linear functions over the interval [5, 6]

What is the asymptote of the graph?

• x=2

• y=-2

• y=0

• y=-1

Tags

CCSS.HSF-IF.C.7D