Lesson 10 5 WarmUp ALGEBRA 1 Graphing Square

Lesson 10 -5 Warm-Up ALGEBRA 1

“Graphing Square Root Functions” (10 -5) What is a “square root function”? Square Root Function: function, f(x), in which the independent variable, x, is inside a radicand Example: y = x (the simplest square root function) y = x+3 y = 2 x - 8 How do you find all of the solutions to a square root function? Since a radicand can’t be negative (you can’t square a negative value), the domain (x values) is limited to those values of x that make the radicand greater than or equal to zero. Therefore, you can create a function table to graph the solutions with x being values that make the expression inside the radicand greater than or equal to zero. To find the minimum value of the range, plug in the minimum value of x that will make the expression in the radical equal zero. Examples: Subtract 3 or add 8 to both sides Make a function table. ALGEBRA 1

Graphing Square Root Functions LESSON 10 -5 Additional Examples Find the domain of each function. a. y = x+5> – 0 Make the radicand > – 0. x> – – 5 The domain is the set of all numbers greater than or equal to – 5. b. y = 6 4 x – 12 > – 0 Make the radicand > – 0. 4 x > – 12 x> – 3 The domain is the set of all numbers greater than or equal to 3. ALGEBRA 1

“Graphing Square Root Functions” (10 -5) How do you graph a square root function? To graph a square root function: 1. Make a function table with at least four x values. Make one of the x values the minimum value of x that makes the expression inside the radicand equal zero. 2. Plot the x and y value on the coordinate grid. 3. Connect the points to form a curve (should look like half of a parabola) Examples: Step 1. Function Table Step 2. Plot the points. Step 3. Connect the points to form a half parabola shape ALGEBRA 1

Graphing Square Root Functions LESSON 10 -5 Additional Examples The size of a television screen is the length of the screen’s diagonal d in inches. The equation d = 2 A estimates the length of a diagonal of a television with screen area A. Graph the function. Domain 2 A > – 0 A> – 0 Screen Area (sq. in. ) 0 50 100 200 300 400 Length of Diagonal (in. ) 0 10 14. 1 20 24. 5 28. 3 ALGEBRA 1

Graphing Square Root Functions LESSON 10 -5 Additional Examples Graph y = y= x + 4 by translating the graph of x. For the graph y = the graph of y = x + 4, x is shifted 4 units up. ALGEBRA 1

Graphing Square Root Functions LESSON 10 -5 Additional Examples Graph ƒ(x) = y= x + 3 by translating the graph of x. For the graph ƒ(x) = the graph of y = x + 3, x is shifted to the left 3 units. ALGEBRA 1

Graphing Square Root Functions LESSON 10 -5 Lesson Quiz 1. Find the domain of the function ƒ(x) = 2. Graph y = 3 3. Graph y = 2 x – 4. x>2 x. x – 3. 4. Describe how to translate the graph of y = x to obtain the graph of the function y = x – 15. Shift the graph to the right 15 units. ALGEBRA 1