Lesson 4

Reflecting Functions

View Student Lesson

Problem 1

The dashed function is the graph of \(f\) and the solid function is the graph of \(g\). Express \(g\) in terms of \(f\).

Graph of function f and g.

Solution

For access, consult one of our IM Certified Partners.

Problem 2

The table gives some values of functions \(f\) and \(g\).

Which of these equations could be true for all values of \(x\)?

\(x\) \(f(x)\) \(g(x)\)
-2 4 \(\frac14\)
-1 2 \(\frac12\)
0 1 1
1 \(\frac12\) 2
2 \(\frac14\) 4
A:

\(f(x) = \text-g(x)\)

B:

\(f(x) = g(-x)\)

C:

\(f(x) = \text-g(-x)\)

D:

\(f(x) = g(x)\)

Solution

For access, consult one of our IM Certified Partners.

Problem 3

Here is the graph of a function \(f\).

Function f on coordinate plane.
  1. On the same axis, sketch a graph of \(f\) reflected over the \(y\)-axis and then translate it 3 units up.
  2. Write an equation (in terms of \(f\)) for a function \(g\) that has the graph that you drew.

Solution

For access, consult one of our IM Certified Partners.

Problem 4

Describe a transformation of the line that contains the two labelled points.

Two points and graph of a line.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 5, Lesson 1.)

Problem 5

The thermostat in an apartment is set to \(75^\circ \text{F}\) while the owner is awake and to \(60^\circ \text{F}\) while the owner is sleeping. The function \(W\) gives the temperature \(W(x)\), in degrees Fahrenheit, in the apartment \(x\) hours after midnight. When it is hot outside, the owner changes the settings to be exactly 10 degrees warmer than \(W\) to save energy. The function \(H\) gives the temperature \(H(x)\), in degrees Fahrenheit, \(x\) hours after midnight when it is hot outside.

  1. If \(W(6.5) = 75\), then what is the corresponding point on \(H\)? Use function notation to describe the point on \(H\).
  2. If \(W(2) = 60\), then what is the corresponding point on \(H\)? Use function notation to describe the point on \(H\).
  3. Write an expression for \(H\) in terms of \(W\).

Solution

For access, consult one of our IM Certified Partners.

(From Unit 5, Lesson 2.)

Problem 6

A ball is hit in the air. Its height \(h\), in feet, \(t\) seconds after it is hit is modeled by the equation \(h = 4 + 50t - 32t^2\). Which equation models the height of a ball following the same path but is hit 2 seconds after the first ball?

A:

\(h = 6 + 50t  - 32t^2\)

B:

\(h = 2 + 50t - 32t^2\)

C:

\(h = 4 + 50(t+2) -32(t+2)^2\)

D:

\(h = 4 + 50(t-2) - 32(t-2)^2\)

Solution

For access, consult one of our IM Certified Partners.

(From Unit 5, Lesson 3.)