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If the graph of x is shifted 7 units up, the equation of the new graph would be: f(x) = x +7.

Transformations in graphs

According to the question:

  • The given equation is: f(x) = x

On this note, when the graph of the equation is shifted 7 units up, it follows that every f(x) value of the graph increases by 7 units.

Hence, the equation of the new graph is; f(x) = x +7.

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The new equation is given by adding 7 to the original equation.

Response:

  • The new equation is; f(x) = x + 7

Which methods can be used to find the new equation?

The given function is f(x) = x

The value by which the graph is shifted up = 7

Required:

The new equation of the graph.

Solution:

The equation, f(x) = x is an equation for a straight line

f(x) = m·x + c

Where;

c = The y-intercept = 0

m = The slope where in the given equation, m = 1

By comparing with the general equation for a straight line, f(x) = mx + c to

the given equation, we have;

The y-intercept, c = 0

When the graph is shifted up 7 units, we have;

c = 0 + 7 = 7

The slope will remain the same, m = 1

The new equation is therefore;

f(x) = 1·x + 7

Which gives;

  • f(x) = x + 7

Learn more about the equation of a straight line here:

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