Transformation of Curves Questions with Solutions

6 questions4 easy2 medium

Transformation of curves is about how the graph of a function changes when its equation is modified. If you know the graph of y = f(x), you can sketch related graphs without plotting points. This topic covers shifts (y = f(x) + k moves the graph up, y = f(x - h) moves it right), reflections in the axes (y = -f(x) and y = f(-x)), stretches and compressions (y = af(x) and y = f(ax)), and graphs involving modulus such as y = |f(x)| and y = f(|x|). Exam questions ask you to identify the graph of a transformed function, find the new position of a point or vertex, or count the solutions of an equation using graphs. A common trap is the direction of horizontal shifts: f(x - 2) moves the graph two units to the right, not the left. Practise the transformation of curves questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
The graph of $y = f (x - 2) + 3$ is obtained from the graph of $y = f (x)$ by shifting it
A. 2 units left and 3 units upB. 2 units right and 3 units upC. 2 units right and 3 units downD. 3 units right and 2 units up
easyView solution ›
Q2.
The vertex of the graph of $y = ∣ x - 1 ∣ + 2$ is at
A. (1, 2)B. (−1, 2)C. (2, 1)D. (1, −2)
easyView solution ›
Q3.
The graph of $y = x^{2}$ is shifted 3 units to the left and then reflected in the x-axis. The equation of the new graph is
A. $y = - (x + 3)^{2}$ B. $y = - (x - 3)^{2}$ C. $y = (x + 3)^{2}$ D. $y = 3 - x^{2}$
mediumView solution ›
Q4.
The graph of $y = f (- x)$ is the reflection of the graph of $y = f (x)$ in
A. the x-axisB. the y-axisC. the originD. the line $y = x$
easyView solution ›
Q5.
The range of $y = 3 s in (2 x - π) + 1$ is
A. [−2, 4]B. [−3, 3]C. [−1, 1]D. [−2, 3]
mediumView solution ›
Q6.
If the graph of $y = (x - 2)^{2} - 3$ is shifted by 5 units up along the y-axis and 2 units to the right along the x-axis, then the equation of the resultant graph is
A. $y = x^{2} + 2$ B. $y = (x - 2)^{2} + 5$ C. $y = (x + 2)^{2} + 2$ D. $y = (x - 4)^{2} + 2$
easyAsked in NIMCET 2017View solution ›