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frika

Answer:

The domain is  [tex](-\infty,\infty)[/tex] and its range is [tex][3,\infty).[/tex]

The y-intercept is (0,3).

Step-by-step explanation:

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

The graph of the function [tex]y=|x|+3[/tex] 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  [tex](-\infty,\infty)[/tex] and its range is [tex][3,\infty).[/tex]

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

[tex]y=|0|+3=3.[/tex]

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

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kudzordzifrancis

Answer:

i)D:[tex]x\in R[/tex]

ii)R: [tex]y\ge3[/tex]

iii) Y-int:(0,3)

Step-by-step explanation:

i) The given absolute value function is;

[tex]f(x)=|x|+3[/tex].

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,

[tex]f(x)=|x|+3[/tex].

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

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

The range is [tex]y\ge3[/tex]

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

[tex]f(0)=|0|+3[/tex].

[tex]f(0)=0+3[/tex].

[tex]f(0)=3[/tex].

The y-intercept is (0,3)

See attachment for graph.

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