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8. (a) Sketch the graph of $y = 7^x$, $x \\in \\mathbb{R}$, showing the coordinates of any points at which the graph crosses the axes - Edexcel - A-Level Maths: Pure - Question 10 - 2011 - Paper 3
Question 10
8. (a) Sketch the graph of $y = 7^x$, $x \\in \\mathbb{R}$, showing the coordinates of any points at which the graph crosses the axes. (b) Solve the equation $$7^x... show full transcript
Worked Solution & Example Answer:8. (a) Sketch the graph of $y = 7^x$, $x \\in \\mathbb{R}$, showing the coordinates of any points at which the graph crosses the axes - Edexcel - A-Level Maths: Pure - Question 10 - 2011 - Paper 3
Step 1
Sketch the graph of $y = 7^x$
Answer
To sketch the graph of the function , we start by identifying key points:
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Intercepts:
- The graph intersects the y-axis at the point (0, 1) since .
- The graph does not cross the x-axis since for all real x.
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Behavior:
- As , approaches 0, and as , increases without bound.
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Sketch:
- Draw a smooth curve starting from the vicinity of (0, 1), approaching the x-axis from above as it moves left, and rising steeply as it moves right.
Step 2