🟥 Unit 9 Review

Part of an exponential function is shown on the graph. Which inequality best represents the domain of the part shown?

• x > 1

• y > 1

• x > 2

• y > 2

Answer explanation

The domain represents the possible x-values (left to right). We can see that the function will continue moving to the right, but what is the furthest this function will ever make it when moving to the left?

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

• all real numbers.
• all real numbers less than 0.
• all real numbers greater than 0.
• all real numbers greater than -2.
• all real numbers less than -2.

Answer explanation

Domain is the set of all possible x-values. Does this function show signs of having an endpoint that it cannot pass to the left or to the right?

Range is the set of all possible y-values. Does this function show signs of having a minimum or maximum value?

• A bacteria population increased by 50 bacteria each hour.

• The bacteria population increased at a rate of 50% each hour.

• The bacteria population decreased at a rate of 50% each hour.

• The bacteria population started with 50 bacteria.

Answer explanation

The format of an exponential function is f(x)=a(b)^x, where "a" represents the initial/starting value and "b" represents the growth or decay factor. To determine the rate of growth or decay, look at the value of b. If b < 1, then the population is decaying at a percentage rate of b times 100. If b > 1, then the population is growing at a percentage rate of (b-1) times 100.

Tags

CCSS.HSF.LE.B.5

• the initial number of trees.
• the decay factor of the number of trees.
• the rate at which the number of trees decrease.
• a percentage increase in trees each year.
• the final number of trees after all the years.

Answer explanation

The format of an exponential function is f(x)=a(b)^x, where "a" represents the initial/starting value and "b" represents the growth or decay factor.

Tags

CCSS.HSF.LE.B.5

A rare plant species is introduced to a greenhouse. Initially, there are 40 plants. The number of plants is expected to increase by 6% each month.

Write an exponential function to model the number of plants , y, after x months.

Mathematical Equivalence

ON

Answer explanation

The format of an exponential function is f(x)=a(b)^x, where "a" represents the initial/starting value and "b" represents the growth or decay factor. If the population is increasing, to find the growth factor you will add 1 to the percentage (written as a decimal). If the population is decreasing, the decay factor will be the percentage written in decimal form.

Tags

CCSS.HSF.LE.A.2

The table represents some points on the graph of an exponential function.

Which function represents the relation shown in the table?

Tags

CCSS.HSF.LE.A.2

An exponential function is graphed on the grid. Which function is best represented by the graph?

Tags

CCSS.HSF.LE.A.2

• The y-intercept is (0, 12).

• The graph is increasing for all values of x.

• The graph has a horizontal asymptote at y = 0.

• The x-intercept is (2, 0).

Answer explanation

Start by graphing the function on desmos. Go through and check each of the answer choices to see if it was true or false. The problem wants to know which answer choice is FALSE.

Tags

CCSS.HSF-IF.C.7E

An exponential function has these characteristics:

The y-intercept is 8.

The function decreases at a rate of 75%.

Which graph best represents this function?

• 
• 
• 
• 

Answer explanation

First, you can eliminate two of the answer choices based on the y-intercept alone.

Next, decide if the graph is growth or decay. If the function is supposed to be increasing, choose the graph that is going up and to the right. If the function is supposed to be decreasing, choose the graph that is going down and to the right.

Tags

CCSS.HSF-IF.C.7E

Mathematical Equivalence

ON

Answer explanation

Remember, the horizontal asymptote is the invisible flat line that the function will approach but never cross. The equation will be in the form y = #.

Tags

CCSS.HSF-IF.C.7D