Advanced MathVery hardZero of a reflected and shifted exponential
Advanced Math practice question
In the xy-plane, the graph of y = 4ˣ is reflected across the x-axis and then shifted up by 16 units. At what value of x does the new graph cross the x-axis?
Answer: 2
The new graph is y = −4ˣ + 16. Setting y = 0 gives 4ˣ = 16, so x = 2.
Common wrong answers
- If you answered 4
- 4 gives −256 + 16.
- If you answered 16
- 16 is the shift, not the zero.
- If you answered -2
- −2 gives 4⁻² = 1/16.
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