Analyzing Intercepts under Function Shifts

00:00 7 marks

Consider the function \(f(x)=x^2\). Solve the following:

(a) Apply a shift to \(f(x)\) that moves the graph 3 units to the right and 2 units up to obtain the new function \(g(x)\).

(b) Find the x-intercepts and y-intercept of the function \(g(x)\).

Part a

3 minutes 3 marks

Question

Apply a shift to the function \(f(x)=x^2\) that moves it 3 units to the right and 2 units up. Write the equation of the new function \(g(x)\).

Hint Hint

Hint

Recall that a right shift by h units and upward shift by k units gives \(g(x)=f(x-h)+k\).

Answer Answer
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Answer Answer

Complete Answer

g(x) = (x-3)^2 + 2

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Part b

4 minutes 4 marks

Question

Find the x-intercepts and y-intercept of the function \(g(x)=(x-3)^2+2\).

Hint Hint

Hint

For x-intercepts, set \(g(x)=0\) and solve; for the y-intercept, evaluate \(g(0)\).

Answer Answer
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Complete Answer

x-intercepts: No real intercepts; y-intercept: \(g(0)=11\)

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