y = mx + b - it's a linear function.
Two points are enough to draw a graph of a linear function.
Step-by-step explanation:
Two different ways.
1.
g(x) = f(x + 1) → put instead of x, x + 1 into function f(x) = 4x - 2:
g(x)=4(x + 1) - 2 use the distributive property
g(x) = 4x + 4 - 2
g(x) = 4x + 2
Choose any two x values. Put them into the equation g(x) = y and calculate the values of y.
x = -1
y = 4(-1) + 2 = -4 + 2 = -2 → (-1, -2)
x = 0
y = 4(0) + 2 = 0 + 2 = 2 → (0, 2)
The graph on the picture #1.
2.
Use the transformation of a graph of a function:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x + n) - shift the graph of f(x) n units to the left
f(x - n) - shift the graph of f(x) n units to the right
f(x) = 4x - 2, g(x) = f(x + 1)
shift the graph of f(x) q unit to the left.
Plot the graph of function f(x).
Choose any two x values. Put them into the equation f(x) = y and calculate the values of y.
x = 0
y = 4(0) - 2 = 0 - 2 = -2 → (0, -2)
x = 1
y = 4(1) - 2 = 4 - 2 = 2 → (1, 2)
Plot the graph of f(x).
Shift it 1 unit to the left.
The graph on the picture #2.
