Find values using function graphs

Learning Objectives Evaluate a function for a specific input value using its graph (e.g., find f(a)). Find the input value(s) for a given function output using its graph (e.g., solve f(x) = b). Determine the domain and range of a function from its graphical representation. Identify the x-intercepts (zeros) and the y-intercept of a function from its graph. Solve equations and inequalities involving one or two functions by analyzing their graphs (e.g., f(x) = g(x) or f(x) > c). Evaluate composite functions using their graphs (e.g., find f(g(2))). Interpret the meaning of function values in the context of a real-world problem represented by a graph. How can a stock market analyst predict trends or a physicist track a particle's movement without a single equation? 📈 T...

TermDefinitionExample Function EvaluationThe process of finding the output value of a function, f(x), that corresponds to a specific input value, x. On a graph, this means finding the y-coordinate for a given x-coordinate.If the point (2, 7) is on the graph of f(x), then evaluating the function at x=2 gives f(2) = 7. DomainThe complete set of all possible input values (x-values) for which the function is defined. Graphically, it is the horizontal extent of the graph.For a graph that starts at x = -5 and ends at x = 3, the domain is the interval [-5, 3]. RangeThe complete set of all possible output values (y-values) that the function can produce. Graphically, it is the vertical extent of the graph.For a parabola with its lowest point at y = -4, the range is [-4, ∞). x-intercept (Zero)A poi...

Finding an Output Value To find f(a), find x = a on the horizontal axis, move vertically (up or down) to the graph, then move horizontally to the vertical axis to read the corresponding y-value. This is the fundamental process for evaluating a function at a specific point using its graph. It answers the question, 'What is the output for this input?' Finding Input Value(s) To solve f(x) = b, find y = b on the vertical axis, move horizontally (left or right) to the graph, then move vertically to the horizontal axis to read the corresponding x-value(s). This process is used to find the input(s) that result in a specific output. Note that there can be one, more than one, or no solutions. Solving f(x) = g(x) The solutions to the equation f(x) = g(x) are the x-coor...