a) The domain and range of the function are x ∈ (- ∞, 8) and y ∈ [- 3, + ∞).
b) The value of f(7) is equal to 2.
c) The values of x such that f(x) = 3 are x₁ = - 8, x₂ = - 1.6, x₃ = 3.
How to analyze a function based on a given graph
In this exercise we analyze and describe a series of features of a function, all derived from a given picture.
a) In the first part we must determine the domain and range of the function, the domain represents the set of values from the horizontal axis that belong that exist in the curve and the range is for the set of values from the vertical axis.
Then, the domain and range of the function are x ∈ (- ∞, 8) and y ∈ [- 3, + ∞).
b) The value of the function corresponds with the point of intersection between x = 7 and y = 2. Hence, the value of f(7) is equal to 2.
c) Now we must find the x-values such that f(x) = 3. After looking in the graph, we find three different solutions: x₁ = - 8, x₂ = - 1.6, x₃ = 3.
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