ACT Math · Function notation and transformations
The function g(x) = f(x-3) + 5 represents what transformation of f(x)?
The function represents what transformation of ?
Answer and explanation
Answer: J: Shift right 3, up 5
In , a number subtracted from inside the function shifts the graph horizontally in the opposite direction from what the sign suggests: shifts the graph right by . A number added outside the function shifts the graph vertically in the direction of the sign: shifts it up by . The transformation is right , up , choice J. Choice F reverses the horizontal shift. Choice H shifts right but down. Choice G shifts left and down. A key point of at moves to .
More Function notation and transformations questions
- Question 15If f(x) = 2x - 3 and g(x) = x² + 1, what is f(g(2))?
- Question 17If f(x) = x² and g(x) = f(x-3) + 2, what is g(5)?
- Question 18A function is defined as f(x) = 2x+1 if x < 2, and f(x) = x²-3 if x ≥ 2. What is f(2) + f(-1)?
- Question 19If f(x) = (3x-5)/(2), what is f^-1(7)?
- Question 20The function f(x) = -2(x-3)² + 7 has its vertex at (3, 7). What is f(5)?
- Question 55A function is defined by the table below. If the pattern continues, what is f(6)?
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