The graph of y=f(x+3) is shown. For which value of x, rounded to the nearest whole number, must f(x)=0 ?

Question

The graph of  y=f(x+3) is shown. For which value of  x, rounded to the nearest whole number, must  f(x)=0 ?

Bytelearn · Accepted Answer

Understand Transformation: To solve for the value of x where f(x) = 0, we need to understand the transformation applied to the function f(x) to get the graph of y = f(x+3). The graph of y = f(x+3) is a horizontal shift of the graph of y = f(x) to the left by 3 units. This means that the x-values on the graph of y = f(x+3) are 3 units less than the corresponding x-values on the graph of y = f(x). To find the x-value where f(x) = 0, we need to look at the graph of y = f(x+3) and find the x-value where the graph crosses the x-axis, and then add 3 to that value.Identify Graph Crossing: Assuming the graph of y = f(x+3) is provided, we would identify the point where the graph crosses the x-axis. Let's say this point is at x = a. This means that f(a+3) = 0. To find the value of x for which f(x) = 0, we need to solve the equation a + 3 = x.Calculate Shifted Value: Without the actual graph, we cannot determine the exact value of a. However, if we had the graph and found that the graph crosses the x-axis at x = a, we would then calculate x by subtracting 3 from a to account for the horizontal shift. So, x = a - 3.Perform Calculation: Once we have the value of a from the graph, we would perform the calculation to find x. For example, if a = -2 (hypothetically), then x = -2 - 3 = -5. We would then round this value to the nearest whole number.Round to Nearest: If x = -5, rounding to the nearest whole number would give us -5 as the final answer, since -5 is already a whole number.

The graph of $y=f(x+3)$ is shown. For which value of $x$ , rounded to the nearest whole number, must $f(x)=0$ ?

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The graph of $y=f(x+3)$ is shown. For which value of $x$ , rounded to the nearest whole number, must $f(x)=0$ ?