NY-F.LE.3

Algebra ILinear and Exponential Models70 target questions

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly quadratically or (more generally) as a polynomial function.

Sample Practice Questions (3)

The graph below shows three functions:

f (x)

g (x)

, and

h (x)

. Which statement correctly identifies the type of function for each graph?

f (x)

is linear,

g (x)

is quadratic,

h (x)

is exponential.

f (x)

is exponential,

g (x)

is linear,

h (x)

is quadratic.

f (x)

is quadratic,

g (x)

is exponential,

h (x)

is linear.

f (x)

is linear,

g (x)

is exponential,

h (x)

is quadratic.

The graph shows a linear function

y = x + 2

and an exponential function

y = 2^{x}

. In which interval is the exponential function greater than the linear function?

x > 2

0 < x < 2

x < 0

DThe linear function is always greater.

Consider the functions

f (x) = 10 x + 100

and

g (x) = 2 (1.5)^{x}

. As

x

increases toward infinity, which statement is true?

f (x)

will eventually exceed

g (x)

because it starts with a larger value.

g (x)

will eventually exceed

f (x)

because exponential growth eventually exceeds linear growth.

f (x)

will always be greater than

g (x)

because the slope is

10

DThe two functions will increase at the same rate for all values of

x

👩‍🏫

Generate a full auto-graded worksheet for NY-F.LE.3 in seconds. Track every student's mastery.

👨‍👩‍👧

See exactly how your child scores on NY-F.LE.3 and get a personalized practice plan.