OBJECTIVE To plot two linear functions and fi nd their point of intersection both graphically and algebraically
Using the same grid, graph the linear functions f (x) = x + 1 and g (x) = 2x − 3 in the domain −1 ≤ x ≤ 5, x ∈ . Use the graph to solve the f (x) = g (x). Verify your answer algebraically.
Solution
As the functions are linear, you need just get two points on each line. Choose the extreme x values of the domain.
x −1 5
f (x) 06 g (x) −5 7
Graph: f (x) = g (x) at x = 4 Algebra: f (x) = g (x)
x + 1 = 2x − 3 1 + 3 = 2x − x 4 = x
y
6 7
3 4 5
1 2
–1 0 –1
–2 –3 –4 –5
1 g (x) 2 3 4 5 6 x
f (x)
EXERCISE 4
1. Draw the following linear functions on graph paper in the given domain for x ∈ :
Note: This is also Activity 2. The activity supplies you with the appropriate grids.
(a) f (x) = x + 1, −1 ≤ x ≤ 5 (b) f (x) = x − 3, −2 ≤ x ≤ 6 (c) f (x) = 2x + 1, −2 ≤ x ≤ 4 (d) f (x) = 4x − 3, −1 ≤ x ≤ 3 (e) f (x) = 1
