1. For h(t) = -6t + 7, determine h-1(4). 2. For the equation describe the parent function and the transformations required to graph the function from its parent function. 3. Use the graph of the function to draw the graph of the inverse. Is the inverse a function? 4. The amount of interest compounded quarterly on a savings deposit of $350 over six years is shown. Explain why the domain and range have a lower limit. Is the relation a function? Explain. 5. Explain what transformations you would need to apply to the graph of function to graph the . 6. Consider the function f(d) = 3d2 - 2d - 11. Determine f(-2), f(-1), f(0), f(1), and f(2). 7. Describe the graph of the relation y = 6. Is the relation a function? Explain your answer. 8. Given the relation x2 + y2 = 16. State the domain and range. Determine whether the relation is a function. Explain your answer. 9. For f(x) = x2, sketch the graph of g(x) = f(-2x + 6). 10. For g(x) = (x + 7)2 + 6x determine x when g(x) = 13. 11. The total profit made by an architectural firm is given by the function P(x) = -x 2 + 70x + 3000 where P(x) represents the profit in thousands of dollars for x number of years. a) Describe the function. b) Determine the maximum possible profit algebraically. Show all of your work. 12. Given f(x) = x2, sketch the graph of g(x) = -f(-5x + 15). Explain the steps you took to sketch your graph and determine the domain and range of the function. 13. Describe the steps needed to graph the equation from its parent function using transformations. 14. Maria wrote that the domain for the function | y 0, R}. Is Maria's answer correct? Explain why or why not. is {x| x 2 R} and the range is {y 4) If the leading coefficient (coefcient of the highest power term) is positive, then there will be a lower limit but no upper limit. IOW, The range is all real numbers greater than or equal to some minimum value. If the leading coefcient is negative, then there will be an upper limit but no lower limit. IOW, The range is all real numbers less than or equal to some maximum value. The relation is not a function 5) You can perform transformations in any order you want, in general. But in this case, you are asking in which order to do them in order to transform f(x) into a specific goal, f(ax+b). The order makes a difference in how you get there. What I do is to explicitly write the steps, one at a time. Suppose we rst do the horizontal shrink f(x) > f(ax). If we then apply a horizontal shift (translation) b units to the left, we would be REPLACING x in f(ax) with x+b, and we'd get f(a(x+b)). That is NOT what we are looking for; it's equal to f(ax+ab). So this order of doing those particular transformations is wrong. If instead we first do the shift, changing x) to f(x+b), and THEN do the shrink, we replace x in x+b with ex, and get f(ax+b), which is what we want. So that is one answer: Start with: f(x) Shift b units to the left: f(x+b) Shrink horizontally by a factor of a: f(ax+b) But in fact we COULD do the two transformations in the other order, if we change the particular amounts. We can write f(ax+b) as f(a(x+bia)}, factoring out the a, and then do this: Start with: f(x) Shrink horizontally by a factor of a: f(ax) Shift bfa units to the left: f(a(x+bl'a)) = f(ax+b) there are a few points that are easily missed. Here are the transformations mentioned on that page: -f(x) reection in the x-axis af(x) vertical stretch by factor a f(x)+a vertical shift up by a f(-x) reection in the y-axis f(ax) horizontal shrink by factor a f(x+a) horizontal shift left by a 4) If the leading coefficient (coefcient of the highest power term) is positive, then there will be a lower limit but no upper limit. IOW, The range is all real numbers greater than or equal to some minimum value. If the leading coefcient is negative, then there will be an upper limit but no lower limit. IOW, The range is all real numbers less than or equal to some maximum value. The relation is not a function 5) You can perform transformations in any order you want, in general. But in this case, you are asking in which order to do them in order to transform f(x) into a specific goal, f(ax+b). The order makes a difference in how you get there. What I do is to explicitly write the steps, one at a time. Suppose we rst do the horizontal shrink f(x) > f(ax). If we then apply a horizontal shift (translation) b units to the left, we would be REPLACING x in f(ax) with x+b, and we'd get f(a(x+b)). That is NOT what we are looking for; it's equal to f(ax+ab). So this order of doing those particular transformations is wrong. If instead we first do the shift, changing x) to f(x+b), and THEN do the shrink, we replace x in x+b with ex, and get f(ax+b), which is what we want. So that is one answer: Start with: f(x) Shift b units to the left: f(x+b) Shrink horizontally by a factor of a: f(ax+b) But in fact we COULD do the two transformations in the other order, if we change the particular amounts. We can write f(ax+b) as f(a(x+bia)}, factoring out the a, and then do this: Start with: f(x) Shrink horizontally by a factor of a: f(ax) Shift bfa units to the left: f(a(x+bl'a)) = f(ax+b) there are a few points that are easily missed. Here are the transformations mentioned on that page: -f(x) reection in the x-axis af(x) vertical stretch by factor a f(x)+a vertical shift up by a f(-x) reection in the y-axis f(ax) horizontal shrink by factor a f(x+a) horizontal shift left by a