Question

Which statement is true of the function f(x) = -3x? Select three options.

The function is always increasing.
The function has a domain of all real numbers.
The function has a range of

Answer 1

The function f(x) = -3x is always decreasing, has a domain of all real numbers, and also has a range of all real numbers. The statement about the function always increasing is false.

Step-by-step explanation:

When considering the function f(x) = -3x, we can evaluate its properties to determine which statements are true. First, since the coefficient in front of x is negative, the function has a negative slope, indicating that it is always decreasing, not increasing. This rules out the first statement.

Second, the domain of this function is indeed all real numbers because there are no restrictions on the values that x can take in the equation. So, the second statement is true.

Third, because x can take on any real number value and there's a constant multiplier of -3, the output can also take on any real number value, but will always be the opposite sign of x or zero. This means the range of the function is also all real numbers. Therefore, the statement about the range is incomplete as provided, but it is true that the range of f(x) is all real numbers.

Answer 2

The function is decreasing.

The domain is all real numbers.

The range is all real numbers.

I can't read your other options.

Step-by-step explanation:

f(x)=-3x is a linear function.

I know this because it is in the form of f(x)=mx+b.

The degree is also 1. If the degree is 1 then the polynomial is linear.

Anyways it is in the slope-intercept form of f(x)=mx+b where m is the slope and b is the y-intercept.

Comparing the following two:

f(x)=mx+b

f(x)=-3x

Tells us the slope is -3 while the y-intercept is 0.

If the slope is negative, the function decreases.

If the slope is positive, the function increases.

If the slope is 0, then it neither increases nor decreases.

So since -3 well is negative, then the function decreases.

Since linear functions are continuous and ours is either decreasing/increase (decreasing), then the function hits every x and y value so the domain and range is all real numbers.