= 4x+28 The function h is defined by h(x). The = graph of y h(x) in the xy-plane has an x-intercept at (a,0) and a y-intercept at (0,b), where a and b are constants. What is the value of a+b?
","rationale_html":"Choice A is correct. The x-intercept of a graph in the xy-plane is the point on the = =4 +28 graph where y 0. It’s given that function h is defined by h^xh x . = =4 +28 Therefore, the equation representing the graph of y h^xh is y x . =4 +28 0=4 +28 Substituting 0 for y in the equation y x yields x . Subtracting 28 -28=4 from both sides of this equation yields x. Dividing both sides of this - = = equation by 4 yields 7 x. Therefore, the x-intercept of the graph of y h^xh in -7,0 = the xy-plane is ^ h. It’s given that the x-intercept of the graph of y h^xh is ,0 =- ^a h. Therefore, a 7. The y-intercept of a graph in the xy-plane is the point on = =4 +28 the graph where x 0. Substituting 0 for x in the equation y x yields =4 0 +28 =28 = y ^ h , or y . Therefore, the y-intercept of the graph of y h^xh in the 0,28 = 0, xy-plane is ^ h. It’s given that the y-intercept of the graph of y h^xh is ^ bh. =28 =- =28 + -7+28 21 Therefore, b . If a 7 and b , then the value of a b is , or . + Choice B is incorrect. This is the value of b, not a b. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the - + + value of a b, not a b.
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