contestada



Suppose that the x-values of the x-intercepts of the graph of y = f(x) are −3 and 2.
What are the x-values of the X-intercepts of the graph of y=f(x+5) ? Write the values on the same line, separated by a comma.

Respuesta :

mhanifa

Answer:

  • The x-intercepts are -8, - 3

================

Given

  • Function y = f(x) with the x-intercepts of - 3 and 2.

To find

  • The x-intercepts of function y = f(x + 5)

Solution

The x-intercept is the value of x, when y = 0, in other words, it is the root of the equation.

According to the x-intercepts, the function is:

  • y = f(x) = (x - (-3))(x - 2) = (x + 3)(x - 2)

The function y = f(x + 5) is then:

  • f(x + 5) = ((x + 5) + 3)((x + 5) - 2) = (x + 8)(x + 3)

The x-intercepts are:

  • x = - 8 and x = - 3
semsee45

Answer:

x = -8, -3

Step-by-step explanation:

Transformations of graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.

Translations

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

f(x) → f(x + 5)  means that the parent function is translated 5 units to the left.

Therefore, if the x-intercepts of the graph y = f(x) are x = -3 and x = 2, the x-values of the intercepts of the graph y = f(x + 5) are:

  • x = -3 - 5  ⇒  x = -8
  • x = 2 - 5  ⇒  x = -3

Learn more about transformations of graphs here:

https://brainly.com/question/27822472

https://brainly.com/question/27845947

Otras preguntas