{"id":236599,"date":"2025-06-16T10:59:01","date_gmt":"2025-06-16T10:59:01","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236599"},"modified":"2025-06-16T10:59:03","modified_gmt":"2025-06-16T10:59:03","slug":"use-the-graph-of-the-function-to-find-the-domain-and-range-of-f","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/use-the-graph-of-the-function-to-find-the-domain-and-range-of-f\/","title":{"rendered":"Use the graph of the function to find the domain and range of f."},"content":{"rendered":"\n

Use the graph of the function to find the domain and range of f. (Enter your answers using interval notation.) y = f() domain range Use the graph to find the indicated function values. (a) f(-1) X (b) f(0) (c) f(1) : (d) f(2)<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let us carefully analyze the graph provided and answer each part accordingly.<\/p>\n\n\n\n

Domain and Range<\/strong><\/p>\n\n\n\n

The domain<\/strong> represents all the x-values for which the function exists. From the graph, the function starts at x=\u22124x = -4x=\u22124 and goes up to x=4x = 4x=4. At x=\u22124x = -4x=\u22124, the point is open, meaning it is not included in the domain. At x=4x = 4x=4, the point is closed, meaning it is included in the domain. Therefore, the domain in interval notation is: (\u22124,4](-4, 4](\u22124,4]<\/p>\n\n\n\n

The range<\/strong> represents all the y-values that the function takes. Observing the graph vertically, the function has its lowest point around y=\u22124y = -4y=\u22124 and goes up to y=6y = 6y=6. Both ends appear to be closed at y=\u22124y = -4y=\u22124 and y=6y = 6y=6. Thus, the range in interval notation is: [\u22124,6][-4, 6][\u22124,6]<\/p>\n\n\n\n

Function Values<\/strong><\/p>\n\n\n\n

Next, we determine the exact function values at the given points:<\/p>\n\n\n\n

(a) f(\u22121)f(-1)f(\u22121): From the graph, at x=\u22121x = -1x=\u22121, the corresponding y-value is y=\u22124y = -4y=\u22124.
Thus, f(\u22121)=\u22124f(-1) = -4f(\u22121)=\u22124.<\/p>\n\n\n\n

(b) f(0)f(0)f(0): At x=0x = 0x=0, the corresponding y-value is y=\u22123y = -3y=\u22123.
Thus, f(0)=\u22123f(0) = -3f(0)=\u22123.<\/p>\n\n\n\n

(c) f(1)f(1)f(1): At x=1x = 1x=1, the corresponding y-value is y=\u22122y = -2y=\u22122.
Thus, f(1)=\u22122f(1) = -2f(1)=\u22122.<\/p>\n\n\n\n

(d) f(2)f(2)f(2): At x=2x = 2x=2, the corresponding y-value is y=0y = 0y=0.
Thus, f(2)=0f(2) = 0f(2)=0.<\/p>\n\n\n\n

Summary of Answers<\/strong><\/p>\n\n\n\n