Question

The graph of f(x) = 0.4x is replaced by the graph of g(x) = 0.4x + k. If g(x) is obtained by shifting f(x) up by 4 units, then what is the value of k? k = 4 k = −4 k equals negative one fourth k equals one fourth

Answer 1

k = 4

Explanation:

Remember if a graph is displaced by a certain number of units, you have to add that number to the equation of the line, in this case the equation was f(x)=0.4x, this means that y will be 0.4 of whatever value is given to x, now if the graph moves up, 4 units, this means that to that equation we have added 4 positive units, so when x is 0, the graph will be in (0,4) and thats the origin of the graph, in the first graph, the origin would be (0,0) since when x=0 y= 0 as well.

Answer 2

The value of k=4

Explanation:

we have

f(x)=0.4x

This function represent a linear direct variation (The line passes through the origin)

we know that

If f(x) is shifting up by 4 units

then

The y-intercept of the function will be the point (0,4)

therefore

The function g(x) will be -----> g(x)=0.4x+4 (equation of the line into slope intercept form)

The rule of the translation

f(x) --------> g(x)

(x,y) -------> (x,y+4)

The translation is 4 units up

therefore

The value of k=4