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6.06 Graphing tangent functions

Adaptive
Worksheet

Interactive practice questions

Consider the equation $y=\tan x$y=tanx.

a

Using the fact that $\tan45^\circ=1$tan45°=1, what is the value of $\tan135^\circ$tan135°?

b

Using the fact that $\tan45^\circ=1$tan45°=1, what is the value of $\tan225^\circ$tan225°?

c

Using the fact that $\tan45^\circ=1$tan45°=1, what is the value of $\tan315^\circ$tan315°?

d

Complete the table of values, giving answers in exact form.

$x$x $0$0 $45^\circ$45° $90^\circ$90° $135^\circ$135° $180^\circ$180°
$\tan x$tanx $0$0 $\editable{}$ undefined $\editable{}$ $\editable{}$
e

Complete the table of values, giving answers in exact form.

$x$x $180^\circ$180° $225^\circ$225° $270^\circ$270° $315^\circ$315° $360^\circ$360°
$\tan x$tanx $0$0 $\editable{}$ undefined $\editable{}$ $\editable{}$
f

Plot the graph of $y=\tan x$y=tanx.

Loading Graph...
Medium
3min

Consider the equation $y=\tan x$y=tanx.

Medium
4min

Consider the equation $y=\tan x$y=tanx.

Medium
4min

Consider the equation $y=\tan x$y=tanx.

Medium
5min
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Outcomes

F.IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

F.IF.C.7.E

Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

F.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

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