Mathematics, 25.06.2019 00:00 thanerose

Holly begins with 1 penny in her piggy bank. she adds 2 pennies on day 1, 4 pennies on day 2, and 8 pennies on day 3. she continues this pattern for 30 days. which statement describes why this sequence is a function? select each correct answer. a) the graph of this sequence would pass the vertical line test. b) each day corresponds to a unique amount of pennies in this sequence. c) the graph of this sequence would pass the horizontal line test. d) each amount of pennies corresponds to a unique day in this sequence.

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Answer from: karlrey4401

All the options are correct.

Step-by-step explanation:

Holly begins with 1 penny in her piggy bank. She adds 2 pennies on day 1, 4 pennies on day 2, and 8 pennies on day 3. She continues this pattern for 30 days.

The pattern which she choses is 2^n where n denotes the number of days.

The graph of this sequence would pass the vertical line test.

" Vertical line test: A function can only have one output, y, for each unique input, x " .

Here also y=2^n and x=n.

Each day corresponds to a unique amount of pennies in this sequence.

Since the sequence is increasing, hence option B is correct.

The graph of this sequence would pass the horizontal line test.

A test use to determine if a function is one-to-one.

As for each n we get a unique value.

Hence, option C is correct.

Each amount of pennies corresponds to a unique day in this sequence.

This option is also true as each amount is a function of number of days.

Answer from: kennyq321

Hey! The answers are actually A) The graph of this sequence would pass the vertical line test. - and- B) Each day corresponds to a unique amount of pennies in this sequence.

I attached a pic as well.

Hope this helps!

Holly begins with 1 penny in her piggy bank. she adds 2 pennies on day 1, 4 pennies on day 2, and 8

Answer from: Quest

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation:

$\newline{\text{the rate of change is change per unit time}}$ $\newline{\text{for (x,y), rate of change is }\frac{y_2-y_1}{x_2-x_1} \text{ or change in y divided by change in x}}$ $\newline{\text{for function 1, the cost goes up by 75-45=30 each time every hour}}$ $\newline{\text{that means that the slope of function 1 is 30 per hour}}$ $\newline{\text{for the 2nd function, 40 is added every hour. therefor, the slope is 40 per hour}}$ $\bigskip\newline{\text{since 40 per hour> 30 per hour, function 2 has a greater rate of change than function 1}}$ $\bigskip\newline{\text{the y intercept is the y value when x is 0}}$ $\newline{\text{for function 1, the y value when x is 0 is 45}}$ $\newline{\text{for function 2, the y value when x is 0 (or the flat rate) is 50}}$ $\newline{\text{since 50> 45, function 2 has a greater y intercept than funciton 1}}$ $\bigskip\bigskip\newline{\text{the answers are: }}$ $\newline{\text{ function 2 has a greater rate of change than function 1}}$ $\newline{\text{function 2 has a greater y-intercept than function 1.}}$