Math functions? Can you help me, please? Consider the functions(see image below):?

Posted on 2017-03-06 18:39:00 in Math by CARIOQUINHA

- In h(x), 𝑎 is a Real Constant and 𝑥 ∈ R, 
- In f (x), 𝑎 is the same Real Constant of the function h(x). 

(I) Show that the graph of the function g(x) does not intersect or touch the eixo axis and find the coordinates (abscissa and ordinate) of the point where the graph of 𝑔 (𝑥) cuts off the Y axis. 

(II) In the function 𝑔 (𝑥), complete the square in the variable 𝑥. 

(III) Sketch the graph of the function g (𝑥), explaining in detail how you have done that. 
Note: IF you only assign some values to the variable 𝑥 and find the corresponding values 𝑓 (𝑥) you are not presenting complete justification for the graph. 

(IV) Find the value of the constant 𝑎 of the function h (𝑥), if we know that h(1) + g (- 2) = 9/2 

(V) For the value of the constant 𝑎 found in (IV), sketch the graph of the function h (𝑥), explaining in detail how you completed this graph. 

(VI) What is the domain of the function 𝑓 (𝑥)? Explain your answer. 

(VII) For the value of the constant 𝑎 found in subitem (IV), sketch the graph of the function 𝑓 (𝑥). Tip: To sketch this graph, use part of the graph of the function g (𝑥) and part of the graph of the function h (𝑥). 

(VIII) Observe the graph of the function h (𝑥) and answer, which is the image of the function 𝑓 (𝑥).

 

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