Exercises: Identifying Transformations of Graphs

For each problem, identify the transformation described and express your answer in the form requested.

Grade 9·21 problems·~30 min·Common Core Math - HS Functions·group·hsf-bf-b-3

Work through problems with immediate feedback

Warm-Up: Review What You Know

These problems review skills you have already learned.

If $f(x) = x^2$ , what is $f(3)$ ?

The graph of $f(x) = x^2$ passes through the point $(2, 4)$ . If every $y$ -value is increased by 5, what is the new point?

$(7, 4)$

$(2, 9)$

$(7, 9)$

$(2, -1)$

A graph is symmetric about the $y$ -axis. If the point $(3, 7)$ is on the graph, which other point must also be on the graph?

$(-3, 7)$

$(3, -7)$

$(-3, -7)$

$(7, 3)$

Apply the transformation rules to identify the effect on the graph.

The point $(4, 7)$ is on the graph of $y = f(x)$ . What is the $y$ -coordinate of the corresponding point on the graph of $y = f(x) + 3$ ?

Which transformation does $y = -2f(x)$ apply to the graph of $y = f(x)$ ?

Shift down 2 units

Vertical stretch by factor 2 and reflection over the $x$ -axis

Horizontal compression by factor 2 and reflection over the $y$ -axis

Vertical compression by factor $\frac{1}{2}$ and reflection over the $x$ -axis

The graph of $y = f(x + 4)$ is the graph of $y = f(x)$ shifted in which direction and by how many units?

Right 4 units

Left 4 units

Up 4 units

Down 4 units

The point $(5, 1)$ is on the graph of $y = f(x)$ . What is the $x$ -coordinate of the corresponding point on the graph of $y = f(x - 3)$ ?

How does the graph of $y = f(3x)$ compare to the graph of $y = f(x)$ ?

Horizontally stretched by a factor of 3 (wider)

Horizontally compressed by a factor of $\frac{1}{3}$ (narrower)

Vertically stretched by a factor of 3

Shifted right 3 units

You're viewing 2 of 6 sections.

Create a free account to continue the full exercise set and save your progress.

0 of 8 answered

Answer all problems to submit.