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a. g(x) = f(x) + 5 b. h(x) = f(x+1)

Suppose that f ( x ) and g ( x ) are functions for which g ( x ) = f ( x ) + 3 for all values of x . a. How are the graphs of f ( x ) and g ( x ) related geometrically?

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a. g(x) = f(x) + 5 b. h(x) = f(x+1)

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  1. Suppose that f(x) and g(x) are functions for whichg(x) =f(x) + 3 for all values of x. a. How are the graphs of f(x) and g(x) related geometrically? b. If f(x) has a local minimum at (–4, –2) and a local maximum at (3, 1), what can be said about local minimum and maximum points for g(x)? c. If f(x) has y-intercept (0, –4), what is the y-intercept of g(x)? d. If f(x) has zeroes at x = 7 and x = –1, what (if anything) can be said about the zeroes of g(x)?

  2. Suppose that f(x) and g(x) are functions for whichg(x) =f(x-3) for all values of x. a. How are the graphs of f(x) and g(x) related geometrically? b. If f(x) has a local minimum at (–4, –2) and a local maximum at (3, 1), what can be said about local minimum and maximum points for g(x)? c. If f(x) has y-intercept (0, –4), what is the y-intercept of g(x)? d. If f(x) has zeroes at x = 7 and x = –1, what (if anything) can be said about the zeroes of g(x)?

  3. 1. Suppose that f(x) and g(x) are functions for whichg(x) =f(3x) for all values of x. a. How are the graphs of f(x) and g(x) related geometrically? b. If f(x) has a local minimum at (–4, –2) and a local maximum at (3, 1), what can be said about local minimum and maximum points for g(x)? c. If f(x) has y-intercept (0, –4), what is the y-intercept of g(x)? d. If f(x) has zeroes at x = 7 and x = –1, what (if anything) can be said about the zeroes of g(x)?

  4. 2. Suppose that f(x) and g(x) are functions for whichg(x) =3f(x)for all values of x. a. How are the graphs of f(x) and g(x) related geometrically? b. If f(x) has a local minimum at (–4, –2) and a local maximum at (3, 1), what can be said about local minimum and maximum points for g(x)? c. If f(x) has y-intercept (0, –4), what is the y-intercept of g(x)? d. If f(x) has zeroes at x = 7 and x = –1, what (if anything) can be said about the zeroes of g(x)?

  5. 3. Find the rule for the function g(x) whose graph is the image of the graph of f(x) under the indicated transformations

  6. 4. The graph of y = f(x) is provided on the coordinate axes in each part of this task. On each coordinate grid, sketch the graph that would result from the indicated transformation of f(x). a. g(x) = f(x) + 5 b. h(x) = f(x+1)

  7. 4. The graph of y = f(x) is provided on the coordinate axes in each part of this task. On each coordinate grid, sketch the graph that would result from the indicated transformation of f(x). a. g(x) = f(x) b. h(x) = 2f(x)

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