Question
The graph of the exponential function g in xy plane passes through the points (0,1), (1,4) and (2,16). Which of the following is NOT true?
- A line can be drawn that does not intersect the graph of g.
- A line can be drawn that intersects the graph of g at exactly one point.
- A line can be drawn that intersects the graph of g at exactly 2 points.
- A line can be drawn that intersects the graph of g at exactly three points.
The correct answer is: A line can be drawn that intersects the graph of g at exactly three points.
Hint:
We will consider the implication of each of the options and eleminate the options that are true.
Step-by-step solution:-
A. A line can be drawn that does not intersect the graph of g.
This option states that a line can be drawn on the given graph that does not intersect graph of g, which is possible as we can see in the adjacent diagram (line a does not intersect with graph of g).
Hence, this option is TRUE and therefore, it is eliminated.
B. A line can be drawn that intersects the graph of g at exactly one point.
This option states that a line can be drawn on the given graph that intersects graph of g at exactly 1 point, which is possible as we can see in the adjacent diagram (line b intersects graph of g at a single point B (1.5,8)).
Hence, this option is TRUE and therefore, it is eliminated.
C. A line can be drawn that intersects the graph of g at exactly 2 points.
This option states that a line can be drawn on the given graph that intersects graph of g at exactly 2 points, which is possible as we can see in the adjacent diagram (line c intersects graph of g at exactly 2 points C1 (0.5,2)& C2 (2,16)).
Hence, this option is TRUE and therefore, it is eliminated.
D. A line can be drawn that intersects the graph of g at exactly three points.
This option states that a line can be drawn on the given graph that intersects graph of g at exactly 3 points, which is NOT POSSIBLE any given line can intersect a curve at maximum 2 points and not more than that.
Hence, this option is FALSE and therefore, it is correct answer.
Final Answer:
Option D i.e. A line can be drawn that intersects the graph of g at exactly three points. is the correct Option.
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?
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Current’s formula: A = 
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