Mathematics, 31.01.2020 04:03 Yek

Graph each absolute value function. state the domain, range, and y-intercept.

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Answer from: KenzieD6032

i)D: $x\in R$

ii)R: $y\ge0$

iii) Y-int:(0,3)

Step-by-step explanation:

i) The given absolute value function is;

f(x)=|x+3| .

The absolute value function is defined for all real values of x.

The domain is all real numbers.

ii) The range is all y-values that will make x defined.

The given function,

f(x)=|x+3| .

has vertex at, (-3,0) and opens upwards.

This implies that, the minimum y-value is 0.

The range is $y\ge0$

iii) To find the y-intercept substitute x=0 in to the function.

f(0)=|0+3| .

f(0)=|3| .

f(0)=3 .

The y-intercept is (0,3)

See attachment for graph.

Graph each absolute value function. state the domain, range, and y-intercept.

Answer from: kyliexhill

The domain is $(-\infty,\infty)$ and its range is $[0,\infty).$

The y-intercept is (0,3).

Step-by-step explanation:

Consider the parent function y=|x|. Its domain is $x\in (-\infty,\infty)$ and its range is $y\in [0,\infty).$

The graph of the function y=|x+3| is obtained from the graph of parent function by translation 3 units to the left (see diagram). This translation doesn't change the domain and the range of the function, thus the domain is $(-\infty,\infty)$ and its range is $[0,\infty).$

To find th y-intercept you have to find y at x=0:

y=|0+3|=|3|=3.

Hence, the y-intercept is (0,3).

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

Answer from: Quest

900 degrees

step-by-step explanation:

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Graph each absolute value function. state the domain, range, and y-intercept.
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