Question

Graph g(x), where f(x) = 4x − 2 and g(x) = f(x + 1)

Answer 1

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.