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Algebra 1: Transformations Name: ______________________________ Day 2 Homework Teacher:_______________ Block_________ REMEMBER: When looking for the change in a linear function's steepness, look at the absolute value of the leading coefficient. General Rules: 1. y = 5x and y = -5x have the same steepness 2. y = -5x is more steep than y = 2x 3. f(x) = -0.5x + 2 is less steep than g(x) = -0.75x – 1 Linear Functions: 1. Write an equation that is LESS STEEP than the function f(x) = 7x ___________________________ 2. Write an equation that is MORE STEEP than the function f(x) = .25x ________________________ Quadratic Functions: 3. Write an equation that is WIDER/LESS STEEP than the function f(x) = x2: _____________________ 4. Write an equation that is WIDER/LESS STEEP than the function f(x) = 4x2: _____________________ 5. Write an equation that is NARROWER/MORE STEEP than the function f(x) = 7x2: ________________ 6. Write the “rule” for the steepness of a quadratic: __________________________________________ ___________________________________________________________________________________ Exponential Functions: 3. Write an equation that is WIDER/LESS STEEP than the function f(x) = 2x: _____________________ 4. Write an equation that is WIDER/LESS STEEP than the function f(x) = ( ) 2x: __________________ 5. Write an equation that is NARROWER/MORE STEEP than the function f(x) = (3)2x: ______________ 6. Write the “rule” for the steepness of an exponential: _______________________________________ ___________________________________________________________________________________ Absolute Value Functions: 7. Write an equation that is WIDER/LESS STEEP than the function f(x) = |3x| _____________________ 8. Write an equation that is NARROWER/MORE STEEP than the function f(x) = _______________ 9. How are the “rules” for absolute value and quadratic similar? ________________________________ ___________________________________________________________________________________ REVIEW: 10. Given y = 4x – 5, write an equation whose graph is reflected and shifted up 6 units. 11. Given y = x – 2, write an equation whose graph is less steep and shifted up 8 units. 12. Given: Function 1 y = - x2 – 4 and Function 2 y = - 3x2 + 2, complete the following sentence (circle the appropriate words and fill in the blank): The graph of Function 2 is less steep / more steep than the graph of function 2, and is shifted up / down _________ units.