Question

are are the functions y = |x| and y = |x| - 5 related

Answer 1

[AI-generated answer — Bot GPT 3.5]

The functions y = |x| and y = |x| - 5 are related in that they are both absolute value functions. However, they differ in terms of their vertical shifting.

The function y = |x| represents a V-shaped graph that starts at the origin (0,0) and opens upwards. It consists of the positive and negative values of x, resulting in a symmetrical graph.

On the other hand, the function y = |x| - 5 is a similar V-shaped graph but has been shifted downward by 5 units. This means that all the corresponding y-values for each x-value in the graph of y = |x| will be decreased by 5 units.

Answer 2

describe how the graphs y = |x| and y = |x + 2| are related

Answer 3

[AI-generated answer — Bot GPT 3.5]

The graphs y = |x| and y = |x + 2| are related because they both represent absolute value functions. However, they differ in terms of their horizontal shifting.

The graph of y = |x| is a V-shaped graph that starts at the origin (0,0) and opens upwards. It consists of the positive and negative values of x, resulting in a symmetrical graph.

Now, let's consider the graph of y = |x + 2|. The "+ 2" inside the absolute value function represents a horizontal shift to the left by 2 units. This means that for any given x-value on the graph of y = |x|, you will substitute (x + 2) into the absolute value function. As a result of this horizontal shift, all the corresponding x-values on the graph of y = |x + 2| will be decreased by 2 units compared to the graph of y = |x|.

In essence, the graph of y = |x + 2| is obtained by taking the graph of y = |x| and shifting it 2 units to the left. Thus, the graph of y = |x + 2| will have the same V-shape as y = |x|, but it will be shifted to the left.

Answer 4

the table shows the Hight of a plant as it grows. what equation in point-slope form gives the plants Hight at any time

3 21
5 35
7 49
9 63

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the equation in point-slope form that gives the plant's height at any time, we can use two points from the table and calculate the slope.

Let's take points (3, 21) and (9, 63) from the table. The first point corresponds to the time 3 and a height of 21, while the second point corresponds to the time 9 and a height of 63.

The slope of the line passing through these two points can be calculated as:

slope = (change in height) / (change in time)
= (63 - 21) / (9 - 3)
= 42 / 6
= 7

Now that we have the slope, we can use the point-slope form equation:

y - y1 = m(x - x1)

Using point (3, 21):

y - 21 = 7(x - 3)

Simplifying this equation, we get:

y - 21 = 7x - 21

y = 7x

Therefore, the equation in point-slope form that gives the plant's height at any time is y = 7x.

Answer 6

write y = - 2/3x + 7 in standard form using integers

Answer 7

[AI-generated answer — Bot GPT 3.5]

To write the equation y = -2/3x + 7 in standard form using integers, we need to eliminate the fraction by multiplying both sides of the equation by 3. This results in:

3y = -2x + 21

Next, we want to rearrange the equation so that the x and y terms are on the same side and the constant term is on the other side. To do this, we can add 2x to both sides:

2x + 3y = 21

Finally, to write the equation in standard form using integers, we typically prefer the coefficient of the x-term to be positive. So, we can multiply both sides of the equation by -1:

-2x - 3y = -21

Therefore, in standard form using integers, the equation y = -2/3x + 7 can be written as -2x - 3y = -21.