# Functions

posted by .

(a)Consider the function:
f(x)=(7x+13)/(13x-1)
(i)Calculate the exact values of the coordinates of the points of intersection of the graph of this function with the coordinate axes.
(ii)Calculate the equations of the asymptotes

(b)The line h(x)=ax+b passes through (-1,-3) and (3,5).
(i)Calculate a and b.
(ii)Solve f(x)<h(x)

help!!!

• Functions -

(a) The function intersects the x axis where f(x) = y = 0. That would be where x = -13/7. It intersects the y axis where x = 0. At that point, the function tells you that y = -13.

There is a vertical asymptote there the denomiator is zero. (x = 1/13). As approaches infinity, f(x) approaces y = 7/13. That is a horizontal asymptote.

(b) Solve ths pair of equations for a and b:
-3 = -a + b
5 = 3a + b

The first step should tell you that a = 2. b = -1 h(x) = 2x -1

Once you have h(x), solve the inequality
(7x + 13)/(13 x-1) < 2x -1

I'll leave that step up to you

## Similar Questions

1. ### Functions

(a)Consider the function: f(x)=(7x+13)/(13x-1) (i)Calculate the exact values of the coordinates of the points of intersection of the graph of this function with the coordinate axes. (ii)Calculate the equations of the asymptotes (b)The …
2. ### Math

What are the similarities and differences between functions and linear equations?
3. ### Math

What are the similarities and differences between functions and linear equations?
4. ### maths - geometry

In a space with an orthonormal coordinate system consider the plane; &: 4x-3y=12 (a)(i)Find the coordinates of the points of intersection of the plane & with the coordinates axes (=axes intersections?
5. ### Math

Consider the functions defined by f(x)=sin2x and g9x)=1/2tanx for x E[-90^0; 180^0] Questions 1. Sketch the graphs of f and g on the same system of axes. 2. Calculate the x-coordinates of the points of intersection of f and g. 3. Determine …
6. ### calculus

Give a reasonable sketch, on the axes provided, of the graph of the function x/(x^2-1)^1/2 showing all characteristics. Use the following pieces to justify your sketch. a) Domain ?
7. ### math

Question-2; Consider the function f(x)= -cos3x -4sin3x. (a)Find the equation of the line normal to the graph of f(x) when x= pie/6 . (b)Find the x coordinates of the points on the graph of f(x) where the tangent to the graph is horizontal. …
8. ### math

The graph of the function f(x)=2^x/a passes through the points (0,b) and (2,0.8). Calculate the values of a and b. Thank you so much for huge help:)))
9. ### Modulus function

Calculate the coordinates of the points of intersection of the graph of y=|2x-3|-2 with the coordinates axes. The answer shows that: y=|2x-3|-2 When X=0, y=3-2=1 I don't get why it is 3, shldnt it be -3?
10. ### algebra

Find the coordinates of the points of intersection of the graph of y=13−x with the axes and compute the area of the right triangle formed by this line and coordinate axes. can u guys plz find answer + explain this problem is …

More Similar Questions