Questions: Graph the function and determine whether the function is one-to-one using the horizontal line test f(x) = x+4 Is the function one-to-one? A. Yes, because there is at least one horizontal line that intersects the graph more than once. B. No, because no horizontal line intersects the graph more than once. C. Yes, because no horizontal line intersects the graph more than once. D. No, because there is at least one horizontal line that intersects the graph more than once.

Solution Steps

The function f(x) = |x + 4| is an absolute value function. Its graph is a V-shape. The vertex of the "V" is at the point where the expression inside the absolute value is equal to zero. x + 4 = 0 which gives x=-4. When x= -4, f(x)=|-4+4|=0. So, the vertex is at (-4,0).

When x=0, f(x)=|0+4|=4. Thus the graph passes through (0,4).

When x=-8, f(x)=|-8+4|=|-4|=4. Thus the graph passes through (-8,4).

Plotting these points and drawing the V-shaped graph, we can visualize the function.

The horizontal line test states that if any horizontal line intersects the graph more than once, the function is not one-to-one. In our case, a horizontal line like _y_ = 4 would intersect the graph of f(x) = |x+4| at two points, (-8, 4) and (0, 4).

Since the horizontal line _y_ = 4 intersects the graph at two points, the function is _not_ one-to-one.

Final Answer: