Additional practice set 2 · Challenge ← Back to lesson

Transformations of Graphs: Additional Practice (Set 2)

12 multiple-choice questions, progressively harder.

Additional practice set 2 · Challenge 0 / 12 answered

Question 1 of 12

1
The rule $y = f(2x - 6)$ transforms $y = f(x)$ . Factoring the input, which describes it?

Answer choices for question 1 A compression by $2$ and shift right $6$ B compression by $2$ and shift right $3$ C stretch by $2$ and shift right $3$ D compression by $2$ and shift left $3$
2
The rule $y = f(3x + 12)$ transforms $y = f(x)$ . Factoring the input, which describes it?

Answer choices for question 2 A compression by $3$ and shift left $12$ B compression by $3$ and shift right $4$ C stretch by $3$ and shift left $4$ D compression by $3$ and shift left $4$
3
The graphs $y = 2f(x) + 3$ and $y = 2(f(x) + 3)$ differ. By what constant vertical amount is the second above the first?

Answer choices for question 3 A $3$ B $0$ , they are the same C $6$ D $1$
4
For $f(x) = x^2 + 4$ , does the compression $y = f(3x)$ equal a vertical stretch $c\,f(x)$ ?

Answer choices for question 4 A No, since $9x^2 + 4 \ne c(x^2 + 4)$ for any $c$ B Yes, with $c = 9$ C Yes, with $c = 3$ D Yes, with $c = 4$
5
'Stretch vertically by $2$ , then shift up $3$ ' gives which rule from $y = f(x)$ ?

Answer choices for question 5 A $y = 2(f(x) + 3)$ B $y = f(2x) + 3$ C $y = 2f(x + 3)$ D $y = 2f(x) + 3$
6
A function $g$ is odd on a domain symmetric about $0$ , and $(4, 7)$ is on its graph. Which point must also be on the graph?

Answer choices for question 6 A $(-4, 7)$ B $(-4, -7)$ C $(4, -7)$ D $(7, 4)$
7
The point $(u, v)$ lies on $y = f(x)$ . Under $y = a f(b(x - h)) + k$ with $b \ne 0$ , where does it land?

Answer choices for question 7 A $\left(bu - h,\ av + k\right)$ B $\left(\tfrac{u}{b} - h,\ av + k\right)$ C $\left(\tfrac{u}{b} + h,\ av + k\right)$ D $\left(\tfrac{u}{b} + h,\ \tfrac{v}{a} + k\right)$
8
The point $(p, q)$ is on $y = f(x)$ . Under $y = a f(b(x - h)) + k$ , where does it land?

Answer choices for question 8 A $\left(bp + h,\ aq + k\right)$ B $\left(\tfrac{p}{b} + h,\ \tfrac{q}{a} + k\right)$ C $\left(\tfrac{p}{b} + h,\ aq + k\right)$ D $\left(\tfrac{p}{b} - h,\ aq - k\right)$
9
Is $f(x) = x^3$ even, odd, or neither, and what invariance does that give its graph?

Answer choices for question 9 A odd; unchanged by a $180^\circ$ rotation about the origin B even; unchanged by reflection across the $y$ -axis C neither; no symmetry D even; unchanged by a $180^\circ$ rotation
10
Reflect $y = f(x)$ across the $x$ -axis, then shift up $2$ . The point $(5, 4)$ on $f$ lands where?

Answer choices for question 10 A $(5, 6)$ B $(5, 2)$ C $(-5, -2)$ D $(5, -2)$
11
With $f(x) = x^2$ , which statement about transforming $y = f(x)$ into $y = 4x^2$ is TRUE?

Answer choices for question 11 A it must be a vertical stretch B it can be described as a horizontal compression by $2$ or a vertical stretch by $4$ C it must be a horizontal compression D the graph reveals which transformation was used
12
The point $(-2, 5)$ is on $y = f(x)$ . Which point must lie on $y = f(-x)$ ?

Answer choices for question 12 A $(-2, -5)$ B $(2, -5)$ C $(2, 5)$ D $(-2, 5)$

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