Common Core Standard HSF-LE.A.1 Questions

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Grade 11 Linear Equations CCSS: HSF-LE.A.1, HSF-LE.A.1a

Given the table below, which lists some of the values of the function

$f(x)$ , which of the following is true, and why?

$\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \$
$-3$	$3/8$
$0$	$3$
$3$	$24$
$6$	$192$
$7$	$384$

The function is linear, since the difference in most x-values is 3 units.
The function is exponential, since the ratio of y-values, over equal intervals, is constant.
It cannot be determined, since the difference in x-values is not constant.
The function is neither linear nor exponential. Both the difference of y-values and the ratio of y-values are not constant for all the values presented in the table.

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

Liz sends a message to her three best friends, Sally, Tim, and Josh. Let this be group one. Each of these three people send the message to three more people. Let this be group two. If this trend continues, the number of messages being sent to each new group of people is increasing at a constant percent.

True
False

Grade 10 Functions and Relations CCSS: HSF-LE.A.1, HSF-LE.A.1a

This question is a part of a group with common instructions. View group »

What is the value of

$Delta f = f(x + Delta x) - f(x)$ , using the definition of

$f(x) ?$ Simplify your answer fully.

$m Delta x + 2b$
$Delta x - 2b$
$m Delta x$
$Delta x + 2m$

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

A car accelerates uniformly on the highway, from 35 mph to 60 mph, in 30 seconds. The speed is increasing at a constant percent each second.

True
False

Grade 10 Functions and Relations CCSS: HSF-LE.A.1, HSF-LE.A.1a

This question is a part of a group with common instructions. View group »

Given the answer in the previous question, which of the following gives the best reasoning as to why one can conclude that a linear function grows by equal differences over equal intervals?

Because the resulting equation for $Delta f$ is also linear, it will increase at a constant rate.
Because there is no slope in the resulting equation, the value of $Delta f$ is constant.
Since the resulting equation for $Delta f$ has no $b$ value, it is independent of the y-intercept. As such, $Delta f$ will increase by equal amounts over equal intervals.
Since $Delta f$ is dependent only on the length of the interval, as long as the interval $Delta x$ is constant, $Delta f$ will be the same.

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

George borrowed some money from a friend. Each month, he pays back 10% of the original amount. The amount George pays each month is decreasing at a constant percent.

True
False

Grade 10 Functions and Relations CCSS: HSF-LE.A.1, HSF-LE.A.1a

This question is a part of a group with common instructions. View group »

What if, for the linear function

$f(x)$ ,

$m =0 ?$

This means that the above reasoning is invalid.
For how the function is defined above, $m$ cannot equal zero.
It makes things easier, since the growth rate of $f(x)$ simply becomes zero (and thus constant) for all intervals.
It does not change anything, since $Delta f$ is not dependent on $m$ .

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

Anne just started working at a new job. The following shows how many sales she has made on each of her first 6 days on the job. Her sales are increasing at a constant percent each day.

$\ \ \ \ \ \ \ \ \ \ \ mathbf{"Number of Days on the Job"} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{"Number of Sales"} \ \ \ \ \ \ \ \ \ \$
$1$	$1$
$2$	$2$
$3$	$4$
$4$	$7$
$5$	$10$
$6$	$14$

True
False

Grade 11 Functions and Relations CCSS: HSF-LE.A.1, HSF-LE.A.1a

This question is a part of a group with common instructions. View group »

Using the definition of

$f(x)$ in the proposition, rewrite

$f(x + \alpha) / f(x)$ , in simplest terms.

$2ab^{x+\alpha}$
$b^{x+2 \alpha}$
$b^alpha$
$\alpha$

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

A meteorite has just entered Earth's atmosphere. A second later, it breaks into two pieces. A second later, each of these two pieces breaks into two pieces. If every second, each piece breaks into two new pieces, then the number of meteor pieces is growing at a constant percent per second.

True
False

Grade 11 Functions and Relations CCSS: HSF-LE.A.1, HSF-LE.A.1a

This question is a part of a group with common instructions. View group »

Which of the following reasons best explains why proposition A is true?

Since $\alpha$ is a constant value, the value of $f(x+\alpha)/f(x)$ will also be a constant value.
Because the simplified form of $f(x+\alpha)/f(x)$ is an exponential equation, it is valid for all values of $x in RR$ , and will be constant.
Since the simplified form of $f(x+\alpha)/f(x)$ is independent of $x$ , it will be a constant value.
Because a constant value to the power of a constant value is also a constant, the value $f(x+\alpha)/f(x)$ will also be a constant value.

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

An environmentalist group is concerned about the fish population in a lake. Each month, they count the number of fish and have recorded the following numbers over the past several months: 400, 380, 360, 340, 320. The number of fish is declining at a constant percent each month.

True
False

Grade 11 Functions and Relations CCSS: HSF-LE.A.1, HSF-LE.A.1a

This question is a part of a group with common instructions. View group »

One way to restate Proposition A is as follows: "Exponential functions grow by equal factors over equal intervals." What is the value of the equal factors and length of the equal intervals as represented in Proposition A?

Equal factors are $x_0$ , equal intervals are $c$ .
Equal factors are $alpha$ , equal intervals are $x$ .
Equal factors are $alpha$ , equal intervals are $c$ .
Equal factors are $c$ , equal intervals are $alpha$ .

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

The signal power of a radio station is inversely proportional to the square of the distance it is away from its source. The power of the signal can therefore be said to decrease at a constant percent each mile one travels away from the the source of the radio transmission.

True
False

Grade 10 Functions and Relations CCSS: HSF-LE.A.1

A car's value depreciates each year by about 15%. Which function would best model the car's value depending on the number of years the owner has had it?

Linear
Exponential
Quadratic
None of the above

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

Atmospheric pressure decreases as you go higher. If the following measurements were made of atmospheric pressure at certain elevations, the decrease in atmospheric pressure is approximately a constant percent per 100 m increase in elevation.

$\ \ \ \ \ \ \ \ \ \ \ mathbf{"Elevation (m)"} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{"Atmospheric Pressure (kPa) "} \ \ \ \ \ \ \ \ \ \$
$0$	$101.3$
$100$	$100$
$200$	$98.7$
$300$	$97.5$

True
False

Grade 10 Functions and Relations CCSS: HSF-LE.A.1

Tom's savings account earns 0.5% simple interest each year. Which type of function would best model the growth of the money in Tom's account over time?

Linear
Exponential
Quadratic
Cubic

Grade 10 Exponents CCSS: HSF-LE.A.1, HSF-LE.A.1c

A 100 g sample of Iodine-131 is left in a secure room. After 1 day, there is 91.7 g of Iodine-131 left. After another day, there is only 84.1 g left. According to these numbers, the amount of Iodine-131 is decreasing approximately at a constant percent per day.

True
False

Grade 10 Functions and Relations CCSS: HSF-LE.A.1

A certain plant will triple the amount of area it covers in a garden each year. Which type of function would best describe the yearly growth of this plant?

Linear
Exponential
Quadratic
None of the above

Grade 10 Functions and Relations CCSS: HSF-LE.A.1

It is raining where Sarah lives, and she is watching a cup that is outside fill with water. Every ten minutes, the water level is 1 cm higher. Which type of function would best describe the increasing water level over time?

Linear
Exponential
Square root
None of the above

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