Find values of functions from graphs

Learning Objectives Find the value of a function, f(x), for a specific input, x, by reading its graph. Find the input value(s), x, for a given function output, f(x). Evaluate arithmetic combinations of functions, such as (f+g)(x) or (f/g)(x), using their graphs. Evaluate composite functions, such as f(g(x)), by sequentially reading values from graphs. Determine the value of a limit (lim x→c f(x)) from a graph, distinguishing it from the function's value at that point, f(c). Approximate the value of a definite integral (∫[a,b] f(x) dx) by interpreting it as the net signed area under the curve. Ever seen a heart monitor in a hospital? 🩺 Doctors read those graphs instantly to understand a patient's condition—they're finding function values in real-time! This tu...

TermDefinitionExample Function Value at a PointThe output of a function for a given input. On a graph, for an input 'c' on the x-axis, the function value f(c) is the corresponding y-coordinate of the point on the curve.If the point (3, 5) is on the graph of f(x), then f(3) = 5. Point of DiscontinuityA point on the graph where the function is not continuous. This can be a 'hole' (a single missing point, also called a removable discontinuity) or a 'jump' (where the graph breaks and continues at a different y-value).A graph might have an open circle at (2, 4), indicating f(2) is undefined, even though the graph approaches a y-value of 4 from both sides. Limit of a Function from a GraphThe y-value that a function's graph approaches as the x-value gets closer...

Evaluating a Function y = f(c) To find the value of a function f(x) at x=c, locate 'c' on the horizontal axis (x-axis). Move vertically until you intersect the graph of the function. Then, move horizontally to find the corresponding value on the vertical axis (y-axis). This y-value is f(c). Arithmetic Combinations of Functions (f \pm g)(c) = f(c) \pm g(c) \quad and \quad (f/g)(c) = f(c) / g(c), g(c) \neq 0 To find the value of a combination of functions at x=c, first find the individual values of f(c) and g(c) from their respective graphs. Then, perform the specified arithmetic operation (addition, subtraction, multiplication, or division). Composition of Functions (f \circ g)(c) = f(g(c)) To evaluate a composite function, work from the inside out. First, f...