Question

The function f(x) = 2x + 6 is given.

(a) Explain what the graph looks like and find
algebraically the points at which it intersects the axes X and Y.
(b) To find algebraically the intersection point of the graphs of f(x) and
of g(x) = −x + 3.
(c) If we know that a straight line passing through the point (2,3) has an inclination equal to
with -1, determine the function of which it is a graphical
presentation.
(d) Prove that the line passing through points (1,3) and (2,-3) is
parallel to graph φ(x) = −6x + 25.

Answer 1

(a) f(x) = 2x + 6 is a linear function.

2x + 6 = 0--->x = -3, so f(x) has an

x-intercept at (-3, 0).

f(0) = 6, so f(x) has a y-intercept at (0, 6).

(b) f(x) = g(x)

2x + 6 = -x + 3

3x = -3, so x = -1

f(x) and g(x) intersect at (-1, 4).

(c) 3 = -1(2) + b

3 = -2 + b, so b = 5

y = -x + 5

(d) m = (-3 - 3)/(2 - 1) = -6

3 = -6(1) + b

3 = -6 + b, so b = 9

y = -6x + 9, so these two lines are

parallel.