Explanation:
Math Resources/
Algebra/
Function
Question
Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 4, 0 and negative 2, negative 10.
-5
-1/5
1/5
5
Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.
Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 4, 0 and negative 2, negative 10.
-5
-1/5
1/5
5
Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k. Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 4, 0 and negative 2, negative 10. -5 -1/5 1/5 5
86
Solution
ANSWER
Answer:
k = -5
The function f(x) passes through the points (-4,0) and (-2,2).
Therefore, the equation of the straight line is given by
\(\frac{}y-2{}{}2-0{} =\frac{}x-(-2){}{}-2-(-4){}\)
⇒ \(\frac{}y-2{}{}2{} =\frac{}x+2{}{}2{}\)
⇒ y = x + 4
⇒ f(x) = x + 4 ......... (1)
Now, g(x) passes through the points (-4,0) and (-2,-10).
Then the equation will be
\(\frac{}y-(-10){}{}-10-0{} =\frac{}x-(-2){}{}-2-(-4){}\)
⇒ \(\frac{}y+10{}{}-10{} =\frac{}x+2{}{}2{}\)
⇒ y = - 5x - 20 = - 5 (x + 4)
⇒ g(x) = -5 (x + 4) ....... (2)
Therefore, from equations (1) and (2) we get k = -5 (Answer)
Answer:
k = -5
The function f(x) passes through the points (-4,0) and (-2,2).
Therefore, the equation of the straight line is given by
�−22−0=�−(−2)−2−(−4)
⇒ �−22=�+22
⇒ y = x + 4
⇒ f(x) = x + 4 ......... (1)
Now, g(x) passes through the points (-4,0) and (-2,-10).
Then the equation will be
�−(−10)−10−0=�−(−2)−2−(−4)
⇒ �+10−10=�+22
⇒ y = - 5x - 20 = - 5 (x + 4)
⇒ g(x) = -5 (x + 4) ....... (2)
Therefore, from equations (1) and (2) we get k = -5 (Answer)