Algebra graphs and functions 4 4 4-5
- 1. Writing a Function Rule and Direct Variation Chapter 4 Lesson 4-4 and Lesson 4-5
- 2. Function Rules You can write a rule for a function by analyzing a table of values. Look for a pattern relating the Independent and dependent variables.
- 3. Writing a Rule form a Table Function Table 8 4 7 3 6 2 5 1 f (x) x
- 4. Write rules for the following tables Remember to look for a pattern 2 4 1 3 0 2 -1 1 f(x) x 4 8 3 6 2 4 1 2 x y
- 5. Application A carpenter buys finishing nails by the pound. Each pound of nails costs $1.19. Write a function rule to describe this relationship. How much do 12 lb of finishing nails cost?
- 6. Direct Variation A function in the form y= kx , where k ≠0, is a direct variation . The constant of variation for direct variation k is the coefficient of x. The variables y and x are said to vary directly with each other.
- 7. Direct Variation For y = kx, y is a function of x. If x = 0, then y = 0, so the graph of a direct variation is a line that passes through (0,0). To tell whether an equation represents a direct variation. Solve for y. If the equation can be written in the form “ y = kx” , where k ≠ 0, it represents a direct variation.
- 8. Is an equation a Direct Variation? Is each equation a direct variation? If it is, find the constant of variation. What form should the equation take? 5x + 2y = 0 7y = 2x 5x + 2y = 9 3y + 4x = 8
- 9. Writing an Equation Given a Point Write an equation of the direct variation that includes the point (4,3) . First start with the function form of a direct variation : y=kx Substitute 4 for x and -3 for y Solve for k Write an equation. Substitute the solution for k in the equation y=kx
- 10. Application Real-World Situation Your distance from lighting varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see lighting, you are about 2 miles from the lighting. Write an equation for the relationship between time and distance.
- 11. Proportions and Equations of Direct Variations You can rewrite a direct variation y = kx as y/x = k. When two sets of data vary directly, the ratio y/x is the constant of variation. It is the same for each data pair.
- 12. Direct Variation and Tables For the table use the ratio y/x to tell whether y varies directly with x. If it does, write an equation for the direct variation. 15 10 12 8 6 4 y/x y x
- 13. Sum it up Write a function rule for the table -1 2 -2 1 -3 0 -4 -1 f(x) x
- 14. Sum it up State the form of a direct variation rule. What does the k represent? State the form of a direct variation proportion. Is each equation a direct variation? I t it is, find the constant of variation. x + 5y = 10 and 3y + 8x = 0 Write an equation of the direct variation that includes the point (-5,-4)