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Algebra / Linear functions Difficulty: Hard

The functions f and g are defined as f(x)= 1 4 x - 9 and g(x)= 3 4 x + 21 . If the function h is defined as h(x)=f(x)+g(x), what is the x-coordinate of the x-intercept of the graph of y=hx in the xy-plane?

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Explanation

The correct answer is -12 . It's given that the functions f and g are defined as fx=14x-9 and gx=34x+21. If the function h is defined as hx=fx+gx, then substituting 14x-9 for fx and 34x+21 for gx in this function yields hx=14x-9+34x+21. This can be rewritten as hx=44x+12, or hx=x+12. The x-intercept of a graph in the xy-plane is the point on the graph where y = 0 . The equation representing the graph of y=hx is y=x+12. Substituting 0 for y in this equation yields 0=x+12. Subtracting 12 from both sides of this equation yields -12 = x , or x = -12 . Therefore, the x-coordinate of the x-intercept of the graph of y=hx in the xy-plane is -12 .