Tanya is given the graphs of the following functions. The functions f(x) and g(x) are linear and the function s(x) is quadratic.
f(x)=3x-8
g(x)=-2x+5
s(x)=4x^2-9x+2
Tanya is then asked to find the graph of (f · g)(x) and the graph of Latex: (g · s)(x) For each combined function, she is given four options to choose from.
What clues will help Tanya identify the correct graph of (f · g)(x)
What clues will help Tanya identify the correct graph of (g · s)(x)
Answers
Step-by-step explanation:
Tanya is given the graphs of the following functions. The functions f(x) and g(x) are linear and the function s(x) is quadratic.
Tanya is then asked to find the graph of (f · g)(x) and the graph of Latex: (g · s)(x) For each combined function, she is given four options to choose from.
What clues will help Tanya identify the correct graph of (f · g)(x)
What clues will help Tanya identify the correct graph of (g · s)(x)
Answer:
(i) (f · g)(x) has linear graph.
(ii) (g · s)(x) has quadratic graph.
Step-by-step explanation:
Given,
f(x) = 3x - 8
g(x) = -2x + 5
s(x) = 4x² - 9x + 2
We need to find the graph of (f · g)(x) and (g · s)(x)
So,
(f · g)(x) = f(g(x)) = 3(-2x + 5) - 8
(f · g)(x) = f(g(x)) = -6x + 15 - 8
(f · g)(x) = f(g(x)) = -6x + 7
Hence, the graph of (f · g)(x) will be linear in nature.
(g · s)(x) = g(s(x)) = -2(4x² -9x + 2) + 5
(g · s)(x) = g(s(x)) = -8x² + 18x -4 + 5
(g · s)(x) = g(s(x)) = -8x² + 18x + 1
Hence, the graph of (g · s)(x) is quadratic in nature.
To know more about the linear graph, click on the link below:
https://brainly.in/question/2869899
To know more about the quadratic graph, click on the link below:
https://brainly.in/question/18908543
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