Question

Explain weather there is a possible transformation of f in the form g(x) =f(x)+k, where k is a constant for which the graph y=g(x) will have no x-intercepts. Enter your answer and your justification in the space provided.

Answer 1

Yes, a transformation of f in the form g(x) =f(x)+k can have no x-intercepts. This will occur if the constant k is added to the y-value of every point on the f(x) graph, resulting in the chart of g(x) being shifted upward by k units. If the original diagram of f(x) had no x-intercepts, then the graph of g(x) would also have no x-intercepts because the x-coordinate of each point on the graph of f(x) is unchanged by the transformation.

Explanation: