14 (a) (i) Sketch the graph of $x = 3$. Show clearly the value of any intercepts. (ii) Sketch the graph of $y = x^2 + 1$. Show clearly the value of any intercepts. (b) Toby has sketched the graph of $y = \frac{1}{x}$ below. Make two comments about the accuracy of his sketch.

GCSE OCR Maths 3D trigonometry: 14 (a) (i) Sketch the graph of $

14 (a) (i) Sketch the graph of $x = 3$ - OCR - GCSE Maths - Question 14 - 2020 - Paper 1

Question 14

14 (a) (i) Sketch the graph of $x = 3$. Show clearly the value of any intercepts. (ii) Sketch the graph of $y = x^2 + 1$. Show clearly the value of any intercepts. ... show full transcript

Worked Solution & Example Answer:14 (a) (i) Sketch the graph of $x = 3$ - OCR - GCSE Maths - Question 14 - 2020 - Paper 1

Step 1

Sketch the graph of $x = 3$. Show clearly the value of any intercepts.

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Answer

To sketch the graph of $x = 3$ , draw a vertical line that passes through the point $(3, 0)$ . This line indicates that for all values of $y$ , $x$ is consistently $3$ . The line intersects the x-axis at the point $(3, 0)$ , confirming that this is the x-intercept. There are no y-intercepts since it never crosses the y-axis.

Step 2

Sketch the graph of $y = x^2 + 1$. Show clearly the value of any intercepts.

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Answer

To sketch the graph of $y = x^2 + 1$ , we start by recognizing that this is a parabola opening upwards. The vertex is at the point $(0, 1)$ . To intercept the y-axis, set $x = 0$ :

y-intercept: $y = (0)^2 + 1 = 1$ So, the y-intercept is $(0, 1)$ . For the x-intercepts, solve for $y = 0$ : $0 = x^2 + 1$ This equation has no real solutions, indicating there are no x-intercepts. The graph remains above the x-axis for all $x$ .

Step 3

Make two comments about the accuracy of his sketch.

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Answer

Toby's sketch should exhibit a hyperbola that approaches the x-axis and y-axis but never touches them, reflecting the asymptotic behavior of $y = \frac{1}{x}$ .
The sections of Toby's sketch in the first and third quadrants are correct, but he must ensure the curve is symmetric about the origin and extends infinitely without touching the axes.

14 (a) (i) Sketch the graph of $x = 3$ - OCR - GCSE Maths - Question 14 - 2020 - Paper 1

Worked Solution & Example Answer:14 (a) (i) Sketch the graph of $x = 3$ - OCR - GCSE Maths - Question 14 - 2020 - Paper 1

Sketch the graph of $x = 3$. Show clearly the value of any intercepts.

Sketch the graph of $y = x^2 + 1$. Show clearly the value of any intercepts.

Make two comments about the accuracy of his sketch.

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