How do you find the domain and range of #y=4absx#?

Answer 1

#x inRR#
#y in[0,+oo)#

#"making a 'quick' sketch of the function will help"#
#"choose values of x and calculate y"#
#color(red)(x=0)toy=4|0|=0to(0,0)#
#color(red)(x=1)toy=4|1|=4to(1,4)#
#color(red)(x=2)toy=4|2|=8to(2,8)#
#color(red)(x=-1)toy=4|-1|=4to(-1,4)#
#color(red)(x=-2)toy=4|-2|to(-2,8)#
#"plotting these points gives"# graph{4|x| [-11.25, 11.24, -5.62, 5.635]}
#"from the graph we can see domain/range"#
#"domain is " x inRR#
#"range is " [0,+oo)#
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Answer 2

The domain of the function y = 4|abs(x)| is all real numbers (-∞, ∞), as there are no restrictions on the values that x can take.

The range of the function depends on the absolute value function. Since the absolute value function always returns a non-negative value, the range of y = 4|abs(x)| is [0, ∞).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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