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4 ● Chapter 2 – Radical Functions Pre-Calculus 12 Solving Radical Equations Solving with a Graphing Calculator Example 1: Solve 6 4 = x x using a graphing calculator. Method 1: Use of a single function. Method 2: Use of a system of two functions. Example 2: Solve 3 5 = + x algebraically. Identify any restrictions on the variables. [ , ] [ , ] [ , ] [ , ]
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Page 1: Solving Radical Equations Solving with a Graphing Calculator ...mathlau.weebly.com/uploads/1/4/9/9/14997226/july_13...Solving Radical Equations Solving with a Graphing Calculator Example

4 ● Chapter 2 – Radical Functions

Pre-Calculus 12

Solving Radical Equations Solving with a Graphing Calculator

Example 1: Solve 64 −=− xx using a graphing calculator.

Method 1: Use of a single function.

Method 2: Use of a system of two functions.

Example 2: Solve 35 =+x algebraically. Identify any restrictions on the variables.

[ , ] [ , ]

[ , ] [ , ]

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Chapter 2 – Radical Functions ● 5

Pre-Calculus 12

Example 3: Solve 392 2=+−+ xx algebraically. Identify any restrictions on the variables.

Example 4: An engineer designs a roller coaster that involves a vertical drop section just below the top of the

ride. She uses the equation advv 2)( 2

0 += to model the velocity, v, in feet per second, of the ride’s cars

after dropping a distance, d, in feet, with an initial velocity, v0, in feet per second, at the top of the drop, and

constant acceleration, a, in feet per second squared. Determine the initial velocity required in a roller coaster

design if the velocity will be 26m/s at the bottom of a vertical drop of 34m. (Acceleration due to gravity in SI

units is 9.8 m/s2).

Assignment: page 96-97 #5-7,9-11

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6 ● Chapter 9 – Rational Functions

Pre-Calculus 12

Rational Functions and Transformations

Definition: A rational function is a function of the form:

)(

)()(

xh

xgxf = , where g(x) and h(x) are polynomials and h(x) ≠ 0.

Definition: Asymptotes – for a graph is a line that the graph approaches. Asymptotes are usually denoted on a graph

as a dotted line.

Examples of rational functions:

xxf

1)( = ,

3

2)(

−=

x

xxg ,

1

2)(

2

2

+=

x

xxh , 272 −+= xxy ,

27

13

2

−−

+

xx

x

Rational Functions can also transform the base rational function, x

y1

= .

khx

ay +

−=

Example 1: Graph i) x

y1

= ii) x

y10

= iii) 23

1+

+−=

xy . Identify the characteristics of the

graphs, including the behavior of the function for its non-permissible value.

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Chapter 9 – Rational Functions ● 7

Pre-Calculus 12

Example 2: Given the graph, write an equation in the form khx

ay +

−= .

Rational Function in the Form of Linear Function over Linear Function

Example 3: Graph the function4

22

+=

x

xy . Identify any asymptotes and intercepts.

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8 ● Chapter 9 – Rational Functions

Pre-Calculus 12

Comparing Rational Functions

Example 3: Consider the functions2

1)(

xxf = ,

2510

3)(

2 +−=

xxxg , and

( )24

16)(

+−=

xxh . Graph each pair

of functions.

• )(xf and )(xg

• )(xf and )(xh

Compare the characteristics of the graphs of the functions.

Assignment: 442-443 #2-7, 10


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