Which of the statements about the graph of the
function y=2x are true? Check all of the boxes
that apply
The domain is all real numbers x because the
exponent of 2 can be any real number
When the x values increases by 1 unit, they
value multiplies by 2
The y-interceptis (0, 1),
The graph never goes below the x axis
because powers of 2 are never negative,
The range is all real numbers

Basically nearly every statement is true except for "the range is all real numbers". The range is actually y > 0 which fits with the graph not going below the x axis. Raising 2 to any real number leads to some positive result. If x = 0, then 2^x = 2^0 = 1 which is why the y intercept is 1.

The second statement can be shown by comparing 2^x with 2^(x+1). Dividing those values leads to [2^(x+1)]/[2^x] = 2^(x+1-x) = 2^1 = 2, meaning that increasing x by 1 has made y twice as large. An example of this would be going from (0,1) to (1,2) then to (2,4) and to (3,8) and so on.

astha8579 astha8579 · Answer 2 · 2022-01-07T12:28:48+01:00

The correct options are

A: The domain is all real numbers x because the exponent of 2 can be any real number,

B: When the x values increases by 1 unit, the y value multiplies by 2

C: The y-intercept is (0, 1).

Given that:

[tex]y = 2^x[/tex]

The first option is correct since any real number can be raised to any real exponent.

The second option is correct since:

[tex]y_1 = f(x) = 2^x\\\\y_2 = f(x+1) = 2^{x+1}\\y_2 - y_1 = 2^x(2-1)\\y_2 = y_1 + 2^x = 2y_1[/tex]

The third option is true since putting x = 0 gives y = 1.

The fourth option is False because y can only assume positive real number values thus the range is [tex]\mathbb{R^+}[/tex].

Thus, we have only option A and C as correct option:

A: The domain is all real numbers x because the exponent of 2 can be any real number,

B: When the x values increases by 1 unit, the y value multiplies by 2

C: The y-intercept is (0, 1).

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https://brainly.com/question/9351490