equation y=-5x+1

Question

I am trying to determine the degree, domain, range, coordinates of x-intercepts, coordinates of y-intercepts, end behavior and number of turning points?

Answer 1

Well this is a linear equation, so the answers are all pretty simple. 

 

The largest power of x is 1, so the degree is 1.

 

The domain is all real numbers, because x can be any number and you will be able to get a value for y.

 

The range is also all real numbers.  Pick any value for y and solve for x.  You will always be able to solve the equation, so that means that y can take on any value.

 

In fact, the domain and range of any linear equation are always the same, all real numbers.

 

To find the y-intercept, set x to 0 and solve for y.  It's easy to see that y = 1, so the y-intercept is (0,1).

 

To find the x-intercept, set y to 0 and solve for x. So you'd have to solve the equation 0 = -5x + 1...

 

5x = 1

x = 1/5

 

So the x-intercept is (1/5,0)

 

The end behavior is that the graph continues on forever is both directions.

 

And a linear equation graphs to a straight line, so there are NO turning points.

 

When you get higher degree polynomials, that's when it gets more interesting!