The graph of $y = f(x)$ is as shown below, with the coordinates of $A$, $B$ and $C$ indicate

Question

The graph of $y = f(x)$ is as shown below, with the coordinates of $A$, $B$ and $C$ indicated. Sketch, on separate diagrams, the graphs of $y = f(x) - 1$, $y = f(2x)$, $y = -f(x - 2)$, $y = \frac{1}{2} f(x)$, $y = |f(x)|$, $y = f(|x|)$ indicating clearly the coordinates of points that correspond to $A$, $B$ and $C$. Source note: the right x-intercept is incorrectly labelled B(0,2), duplicating the vertex label. Its intended name is C in the text, but its exact x-coordinate is not supplied reliably. Write $C=(c,0)$, with $c>0$; no value of c or exact curve equation is inferred from the drawing.

Accepted Answer

(a) $A(-2,-1),B(0,1),C(c,-1)$. (b) $A(-1,0),B(0,2),C(c/2,0)$. (c) $A(0,0),B(2,-2),C(c+2,0)$. (d) $A(-2,0),B(0,1),C(c,0)$. (e) A, B, C unchanged. (f) $B(0,2)$, intercepts $(\pm c,0)$; original A is discarded. The source does not specify c reliably.

Transformations of Graphs - Composite Transformations

Transformations of Graphs - Composite Transformations

Solution:

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