Single transformation between given equations

OCR MEI C1 Q7

7

Describe fully the transformation which maps the curve $y = x ^ { 2 }$ onto the curve $y = ( x + 4 ) ^ { 2 }$.
Sketch the graph of $y = x ^ { 2 } - 4$.

OCR MEI C1 Q6

6

Describe fully the transformation which maps the curve $y = x ^ { 2 }$ onto the curve $y = ( x + 4 ) ^ { 2 }$.
Sketch the graph of $y = x ^ { 2 } - 4$.

OCR MEI C2 Q5

5 State the transformation which maps the graph of $y = x ^ { 2 } + 5$ onto the graph of $y = 3 x ^ { 2 } + 15$.

OCR MEI C1 2010 January Q4

4

Describe fully the transformation which maps the curve $y = x ^ { 2 }$ onto the curve $y = ( x + 4 ) ^ { 2 }$.
Sketch the graph of $y = x ^ { 2 } - 4$.

AQA C2 2012 June Q9

9 The diagram shows part of a curve whose equation is $y = \log _ { 10 } \left( x ^ { 2 } + 1 \right)$.
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Use the trapezium rule with five ordinates (four strips) to find an approximate value for $$\int _ { 0 } ^ { 1 } \log _ { 10 } \left( x ^ { 2 } + 1 \right) d x$$ giving your answer to three significant figures.
The graph of $y = 2 \log _ { 10 } x$ can be transformed into the graph of $y = 1 + 2 \log _ { 10 } x$ by means of a translation. Write down the vector of the translation.
1. Show that $\log _ { 10 } \left( 10 x ^ { 2 } \right) = 1 + 2 \log _ { 10 } x$.
2. Show that the graph of $y = 2 \log _ { 10 } x$ can also be transformed into the graph of $y = 1 + 2 \log _ { 10 } x$ by means of a stretch, and describe the stretch.
3. The curve with equation $y = 1 + 2 \log _ { 10 } x$ intersects the curve $y = \log _ { 10 } \left( x ^ { 2 } + 1 \right)$ at the point $P$. Given that the $x$-coordinate of $P$ is positive, find the gradient of the line $O P$, where $O$ is the origin. Give your answer in the form $\log _ { 10 } \left( \frac { a } { b } \right)$, where $a$ and $b$ are integers.

AQA C2 2013 June Q5

5

Use the trapezium rule with five ordinates (four strips) to find an approximate value for $\int _ { 0 } ^ { 2 } \sqrt { 8 x ^ { 3 } + 1 } \mathrm {~d} x$, giving your answer to three significant figures.
Describe the single transformation that maps the graph of $y = \sqrt { 8 x ^ { 3 } + 1 }$ onto the graph of $y = \sqrt { x ^ { 3 } + 1 }$.
The curve with equation $y = \sqrt { x ^ { 3 } + 1 }$ is translated by $\left[ \begin{array} { c } 2
- 0.7 \end{array} \right]$ to give the curve with equation $y = \mathrm { g } ( x )$. Find the value of $\mathrm { g } ( 4 )$.
(3 marks)