Question

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, the y-value multiplies by 2. The y-intercept is (0, 1). The graph never goes below the x-axis because powers of 2 are never negative. The range is all real numbers.

Answer 1

Answer:

The correct options are 1, 2, 3 and 4.

Step-by-step explanation:

The given function is

$f(x)=2^x$

The above function is defined for all the values of x.

⇒ Therefore the domain is all real numbers x because the exponent of 2 can be any real number.

⇒ The x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.

Put x=0, to find the y-intercept.

$f(x)=2^=1$

⇒The y-intercept is (0, 1).

The value of f(x) is always greater than 0 because powers of 2 are never negative.

$f(x)>0$

⇒The graph never goes below the x-axis because powers of 2 are never negative.

⇒Therefore the range of the function is all positive real numbers.

Therefore the correct options are 1, 2, 3 and 4.

Answer 2

Answer:

-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, the y-value multiplies by 2.

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

-The graph never goes below the x-axis because powers of 2 are never negative