two functions are defined as follows: f(x)=3/x+1 and g(x)=x-6
a) Write the equations of the vertical and horizonal asymptotes of f.
b) Determine the coordinates of the points where f(x) = g(x)
Thank you so much for huge help
Is ti correct please?
answer for a) vertical asympt.: -1
horizontal asympt.: y = 0
gor g is vertical asympt.: 6
horizon asympt: -6
b) x^2-5x-9 = 0
now I need to find two roots, right?
Thank you so much for help, I have no idea, please help me:)))
a) the vertical asymptote equation is
x = -1 , you had just -1 , but it asked for the equation.
your horizontal asymptote is correct
g(x) = x-6 is a straight line, with no asymptotes.
b), yes , find the roots ...
3/(x+1) = x-6
x^2 -5x - 6 = 3
x^2 - 5x - 9 = 0
does not factor, so let's use the formula
x = (5 ± √61)/2
= appr 6.405 or -1.405
Thank you so much . a)Equation is x=-1vertical asympt. Is it correct please?
yes, that is what I had stated in my reply.
a) To determine the equations of the vertical and horizontal asymptotes of the function f(x) = 3/x + 1, we need to analyze the behavior of the function as x approaches positive or negative infinity.
Vertical asymptote: When looking at the function f(x) = 3/x + 1, we can see that the denominator x approaches 0 as x approaches positive or negative infinity. Therefore, the vertical asymptote of f(x) is x = 0.
Horizontal asymptote: To determine the horizontal asymptote, we compare the degrees of the numerator and denominator of the function. In this case, the numerator has a degree of 0, and the denominator has a degree of 1. Since the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is at y = 0.
So, the correct answer for the vertical asymptote is x = 0 and for the horizontal asymptote is y = 0.
b) To find the coordinates of the points where f(x) = g(x), we need to set the two functions equal to each other and solve for x.
Setting f(x) equal to g(x), we have 3/x + 1 = x - 6. Moving all terms to one side, we get 3/x - x + 7 = 0.
To solve this equation, you can use various methods such as factoring, using the quadratic formula, or graphing. However, the equation you mentioned, x^2 - 5x - 9 = 0, does not seem to correspond to the equation we obtained above.
Please double-check the equation you provided and reconfirm the equation you want to solve. Once you have the correct equation, you can proceed to find the roots, which will give you the x-coordinates of the points where f(x) = g(x).