Question

Which function could be represented by the graph on the coordinate plane?

a. (f(x) = (x - 3)² + 6)
b. (f(x) = (x + 8)² + 6)
c. (f(x) = (x + 3)² -6)
d. (f(x) = (x-8)²-6)

Answer 1

The graph could be represented by the function f(x) = (x + 3)² - 6. Therefore, option c. (f(x) = (x + 3)² -6) could be represented by the given graph,

Step-by-step explanation:

The given graph starts at a positive value and has a positive slope that decreases with increasing x. option c. (f(x) = (x + 3)² -6) could correspond to this graph.

Let's compare the characteristics of this graph with the given information:

• The graph starts at a positive value:
• When x = 0, f(x) = (0 + 3)² -6 = 3² -6 = 9 - 6 = 3, which is positive.
• The graph has a positive slope that decreases with increasing x:
• The fact that the graph is a quadratic function and opens upwards indicates a positive slope.
• Additionally, the larger the value of x, the smaller the slope becomes, which demonstrates a decrease in magnitude.

Therefore, option c. (f(x) = (x + 3)² -6) could be represented by the given graph .