Question 2 of 10
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) = ?
f(x) = x2
w
g(x) =

Answer: it’s c

Step-by-step explanation:

Just took it and it’s correct

The equation of graph of the transformed function is g ( x ) = ( x + 4 )² - 3

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) = x²

Let the second function be g ( x )

Now , the vertex of the function is at A ( -4 , -3  )

When the function is shifted left by 4 units and down by 3 units , we get

g ( x ) = ( x + 4 )² - 3

Hence , the transformed function is g ( x ) = ( x + 4 )² - 3 and the graph is plotted

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