Kim's flower was 2 inches high when she got it. It grew 0.75 inches per month until it was 12 months old. She keeps track of her flower's growth on a coordinate grid by graphing its height every two months and connecting the points to show the growth in between months.
Which statements are true? (Choose 4)
Responses
The Domain is [2, 11] and the Range is [0, 12]
The Domain is [2, 11] and the Range is [0, 12]
The Domain is [- infinity, 12] and the Range is [2, infinity]
The Domain is [- infinity, 12] and the Range is [2, infinity]
The function is discrete.
The function is discrete.
The function is decreasing over time.
The function is decreasing over time.
The function is increasing over time.
The function is increasing over time.
The function is Linear.
The function is Linear.
The Domain is [0, 12] and the Range is [2, 11]
The Domain is [0, 12] and the Range is [2, 11]
The function is Nonlinear.
The function is Nonlinear.
The functions is continuous.
The functions is continuous. (Note: this statement is not necessarily true since the function is discrete and only takes on specific, isolated values at certain points in time)
Kim's flower was 2 inches high when she got it. It grew 0.75 inches per month until it was 12 months old. She keeps track of her flower's growth on a coordinate grid by graphing its height every two months and connecting the points to show the growth in between months.
Based on this information, the following statements are true:
- The Domain is [0, 12] (inclusive of both 0 and 12), representing the time in months since Kim got the flower.
- The Range is [2, 8.5] (inclusive of both 2 and 8.5), representing the height of the flower in inches at different points in time.
- The function is discrete because it only takes on specific, isolated values every 2 months (e.g. 2 inches at month 0, 3.5 inches at month 2, 5 inches at month 4, etc.).
- The function is increasing over time because the height of the flower is getting bigger as time goes on.
- The function is nonlinear because it does not follow a straight line on the graph, but rather forms a curved shape as the flower grows at a constant rate per month.
- The function is continuous between the plotted points (i.e. the height of the flower) but not continuous across the entire domain (i.e. at every decimal point between whole numbers) because the function is discrete.
Which of the following functions has the values of the range decrease as the values in the domain increase?
Responses
f(x)= 2x − 15
f(x)= 2x − 15
f(x) = 12x − 15
f(x) = 12x − 15
f(x)= 15x − 2
f(x)= 15x − 2
f(x) = −2x + 15
f(x) = -2x + 15 has the values of the range decrease as the values in the domain increase.
Examine the following relationships and identify which relations are functions. Select all that apply.
Responses
x y
1 -10
2 -4
3 -1
4 2
5 -4
This relationship is a function since it has a unique output (y-value) for each input (x-value).
Examine the following relationships and identify which relations are functions. Select all that apply.
Responses
f(x) = -x^4 - 1
This is a function as well since each input (x-value) produces a unique output (y-value).
Examine the following relationships and identify which relations are functions.
(0, 4) (1, 5) (2, 6) (3, 7) (10, 7)
This relationship is a function since it has a unique output (y-value) for each input (x-value), except for the input values of 10 and 7. However, since a function can have repeated output values, the relationship can still be considered a function.
A line is parallel to the y-axis on a coordinate plane. Which best describes the slope of the line?
Responses
positive
positive
negative
negative
undefined
undefined
zero
\
The slope of a line parallel to the y-axis is undefined, since it does not have a change in y for any change in x.
Bill calculates his annual commission, y, using the model y = 0.40x, where x represents his total sales for the year. What is the meaning of the y-intercept in the model?
Responses
the y-intercept represents Bill's commission pay when he had zero total sales
the y-intercept represents Bill's commission pay when he had zero total sales
the y-intercept represents the highest salary Bill can earn
the y-intercept represents the highest salary Bill can earn
the y-intercept represents Bill's total sales when he earned no commission
the y-intercept represents Bill's total sales when he earned no commission
the y-intercept represents Bill's base pay
The y-intercept represents Bill's commission pay when he had zero total sales, since it is the starting point of the equation when x is equal to 0.
The price of bread went from $1.75 per loaf when Sally started tracking it to $3.50 per loaf in five years. Find the rate of change of the price of bread.
Responses
$1.75 per year
$1.75 per year
$0.35 per year
$0.35 per year
$0.75 per year
$0.75 per year
$0.25 per year
The rate of change of the price of bread can be calculated by finding the difference in price and dividing it by the number of years:
(3.50 - 1.75) / 5 = 0.35
Therefore, the rate of change of the price of bread is $0.35 per year.
Which graph represents the equation f(x)=4x −2
?
The graph of the equation f(x) = 4x - 2 is a straight line with a slope of 4, passing through the point (0, -2). It can be represented by the graph:
```
|
8 -
|
6 -
|
4 - +
| /
2 - /
| /
0 -+--------->
0 1 2 3 4
```
Put the items in order from least steep to steepest rate of change.
Susie has $200 in her savings account. She plans to spend $5 per week until she has a total of $100
Jim's puppy weighed 4 pounds when it was born. It gained 3 pounds per month until it was 9 months old
f (t) = -10x + 5
g(x) = 15x + 1
Ordering the items from least steep to steepest rate of change:
- Susie spending $5 per week from her initial savings of $200 until she has a total of $100, which is a decrease of $100 over 20 weeks. This gives a rate of change of -5 dollars per week.
- Jim's puppy gaining 3 pounds per month for 9 months, which is an increase of 27 pounds over 9 months. This gives a rate of change of 3 pounds per month.
- The function f(x) = -10x + 5, which has a slope of -10 and represents a steep rate of change. This means that for each unit increase in x, the corresponding y-value decreases by 10 units.
- The function g(x) = 15x + 1, which has a slope of 15 and represents a steep rate of change. This means that for each unit increase in x, the corresponding y-value increases by 15 units.
The rain began and increased quickly to a heavy rain, then remained heavy and finally tapered off. Which graph models the situation?
The graph that models this situation would show an increase in the rate of change, followed by a period of constant high rate of change, then a decrease in the rate of change. This could be represented by a bell-shaped curve or a more triangular shape.
Here is an example of a graph that would model the situation described:
```
/\
/ \ /\
/ \_______/ \
/ \
---------------------------->
time
```
The curve would start at a low point and gradually increase to a peak, before gradually decreasing back down to a low point again. This shape represents the rain starting slowly, then quickly increasing to a heavy rain, remaining heavy, then slowly tapering off.