Transforming graphs
Types of exercises: shifting the graph of a function, properties of a function after shifting its graph.
Exercises are drawn at random from a large bank - every click gives a different set.
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Give the zeros of the function g
The function f has exactly two zeros: −2 and 0. The function g is given by g(x) = f(x + 1).
Give the formula of the function g in general form
The graph of f(x) = x² was shifted 3 units to the left and 4 units up. The result is the graph of a function g.
Give the coordinates of the vertex of the parabola that is the graph of the function g
The graph of the function f is a parabola with vertex (1, −1). The function g is given by g(x) = f(x − 4) − 2.
Give the formula of the function g in general form
The graph of f(x) = x² was shifted 4 units to the right and 15 units down. The result is the graph of a function g.
Give the range of the function g
The range of the function f is the interval [2, 5]. The function g is given by g(x) = f(x − 5).
Give the formula of the function g in general form
The graph of f(x) = x² was shifted 7 units to the right and 15 units up. The result is the graph of a function g.
Give the domain of the function g
The domain of the function f is the interval [2, 11]. The function g is given by g(x) = f(x) + 6.
Give the formula of the function g in general form
The graph of f(x) = x² was shifted 1 unit to the right and 2 units up. The result is the graph of a function g.
Give the zero of the function g
The graph of the function f(x) = −2x − 2 was shifted 6 units up. This gave the graph of the function g.
Give the formula of the function g in general form
The graph of f(x) = x² was shifted 1 unit to the right and 15 units down. The result is the graph of a function g.
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