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kompoz [17]
3 years ago
14

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

Mathematics
2 answers:
SVEN [57.7K]3 years ago
5 0

Answer:

The domain is  (-\infty,\infty) and its range is [3,\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 up (see diagram). This translation doesn't change the  domain and will change the range of the function, thus the domain is  (-\infty,\infty) and its range is [3,\infty).

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

y=|0|+3=3.

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

EastWind [94]3 years ago
5 0

Answer:

i)D:x\in R

ii)R: y\ge3

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, (0,3) and opens upwards.

This implies that, the minimum y-value is 3.

The range is y\ge3

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

f(0)=|0|+3.

f(0)=0+3.

f(0)=3.

The y-intercept is (0,3)

See attachment for graph.

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