Question

Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.

A.) 3
B.) 1/3
C.) -1/3
D.) -3

Answer 1

Answer:

-3 is the value of k in g(x)=kf(x)

Step-by-step explanation:

Both functions cross nicely at x=-3 so I'm going to plug in -3 for x:

g(x)=kf(x)

g(-3)=kf(-3)

To solve this for k we will need to find the values for both g(-3) and f(-3).

g(-3) means we want the y that corresponds to x=-3 on the curve/line of g.

g(-3)=-3

f(-3) means we want the y that corresponds to x=-3 on the curve/line of f.

f(-3)=1

So our equation becomes:

g(-3)=kf(-3)

-3=k(1)

-3=k

So k=-3.

Answer 2

This is about interpretation of graphs.

Option C is correct.

• From the graph, we can see the 2 lines representing function f(x) and function g(x).

• Now for us to find the value of x in g(x) = k⋅f(x), we need get a mutual x-coordinate where we can easily read their respective y-coordinate values.

We see that the best point for that is where x = -3.

• For f(x), when x = -3, y = 1

• For g(x), when x = -3, y = -3

we can rewrite them as;

x = -3, f(-3) = 1 and x = -3, g(-3) = -3

• Let us plug in the relevant values into g(x) = k⋅f(x) to get;

-3 = k(1)

Thus; k = -1/3

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