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2 years ago

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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 re

al 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.

2 answers:

aev [14]2 years ago

8 0

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.

Hitman42 [59]2 years ago

6 0

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

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Need some help working these out

s2008m [1.1K]

Answers:

Problem 1) 40 degrees
Problem 2) 84 degrees
Problem 3) 110 degrees

===============================================

Explanation:

For these questions, we'll use the inscribed angle theorem. This says that the inscribed angle is half the measure of the arc it cuts off. An inscribed angle is one where the vertex of the angle lies on the circle, as problem 1 indicates.

For problem 1, the arc measure is 80 degrees, so half that is 40. This is the measure of the unknown inscribed angle.

Problem 2 will have us work in reverse to double the inscribed angle 42 to get 84.

-------------------

For problem 3, we need to determine angle DEP. But first, we'll need Thales Theorem which is a special case of the inscribed angle theorem. This theorem states that if you have a semicircle, then any inscribed angle will always be 90 degrees. This is a handy way to form 90 degree angles if all you have is a compass and straightedge.

This all means that angle DEF is a right angle and 90 degrees.

So,

(angle DEP) + (angle PEF) = angle DEF

(angle DEP) + (35) = 90

angle DEP = 90 - 35

angle DEP = 55

The inscribed angle DEP cuts off the arc we want to find. Using the inscribed angle theorem, we double 55 to get 110 which is the measure of minor arc FD.

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