![]() ![]() Next, we can use the point-slope formula to find the equation for q. We know two points on q, so if we determine the slope of q, we can then use the point-slope formula to find the equation of q.įirst, let's find the slope between (3, –4) and (–6, 2) using the formula for slope between the points (x 1, y 1) and (x 2, y 2). ![]() As a result, since m passes through (–4, 3) and (2, –6), when m is reflected across y = x, the points it will pass through become (3, –4) and (–6, 2).īecause line q is a reflection of line m across y = x, q must pass through the points (3, –4) and (–6, 2). Thus, if line m is reflected across the line y = x, the points that it passes through will be reflected across the line y = x. In other words, the point (a, b) reflected across the line y = x would be (b, a). When a point is reflected across the line y = x, the x and y coordinates are switched. The three transformations of f( x) can be represented as – f( x + 4) – 5. Thus, a downward shift of 5 to the function – f( x + 4) would be represented as – f( x + 4) – 5. In general, if g( x) is a function, then g( x) + h represents a shift upward if h is positive and a shift downward if h is negative. The final transformation requires shifting the function down by 5. Thus, after – f( x) is shifted to the left by four, we can write this as – f( x – (–4)) = – f( x + 4). In order, to shift the function to the left by four, we would need to let h = –4. If h is positive, then the shift is to the right, and if h is negative, then the shift is to the left. In general, if g( x) is a function, then g( x – h) represents a shift by h units. Next, the function is shifted to the left by four. Thus, – f( x) represents f( x) after it is reflected across the x-axis. This can be represented by multiplying f( x) by –1. This kind of transformation takes all of the negative values and makes them positive, and all of the positive values and makes them negative. The first transformation is the reflection of f( x) across the x-axis. ![]() F( x) undergoes a series of three transformations. ![]()
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