Desmos Art Project - Template

This equation represents a transformation of the parent function y=x^ {2}. Firstly, the term −(0.6m(x−6.6)) ^2 introduces horizontal compression, translation, and reflection. The coefficient m adjusts the horizontal stretch or compression, potentially flipping the graph over the x-axis if negative. Additionally, the term x−6.6 shifts the graph horizontally along the x-axis. Secondly, the constant term 7.3 results in a vertical translation, lifting the entire graph by 7.3 units along the y-axis. Additionally, the inequality 4.86<x<8.222 restricts the domain of the function to values between 4.86 and 8.222. Furthermore, the slider m, ranging from −10 to 10, allows for dynamic adjustments to the horizontal compression, stretch, or reflection of the graph. Overall, these transformations combine to produce a horizontally compressed, translated, and potentially reflected version of the original quadratic function y=x^2, with the domain restricted to values between 4.86 and 8.222, and the slider m providing further control over the horizontal compression, stretch, or reflection of the graph.

The equation represents a transformation of the parent function 1=\frac {x^ {2}} {c^ {2}} +\frac{y^ {2}} {d^ {2}}. Firstly, the terms \frac{\left(114x-720\right) ^ {2}} {45c^ {2}} and \frac{\left(225y-1305\right) ^ {2}} {300i^ {2}} introduce horizontal and vertical compression/stretch. The coefficients 45c^2 and 300i^2 control the scale of compression/stretch along the respective axes. Secondly, the terms 114x−720 and 225y−1305 introduce horizontal and vertical translations, respectively, adjusting the position of the ellipse along the axes. Furthermore, the inequality ≤r^2 adjusts the radius of the ellipse. The slider labeled "r" controls the radius and ranges from -10 to 10. Moreover, the sliders labeled "c" and "i" control the parameters c and i. Ranging from -10 to 10, they adjust the horizontal and vertical compression and stretch of the ellipse. Overall, these transformations combine to produce an ellipse with horizontal and vertical compression/stretch, translation along the axes, and adjustable radius. The sliders for "r", "c", and "i" provide dynamic control over the size and shape of the ellipse.

This equation represents a transformation of the parent function y=∣x∣. Firstly, the term −∣2x−19.9∣ introduces a reflection across the x-axis and horizontal compression of the graph by a factor of 1/2. This compression narrows the graph horizontally. Secondly, the constant term 13.768 results in a vertical translation, raising the entire graph by 13.768 units along the y-axis. Furthermore, the inequality 13.47<y restricts the range of the function, ensuring that the y values are greater than 13.47. Overall, these transformations combine to produce a horizontally compressed and vertically shifted version of the original absolute value function y=∣x∣, with the range restricted to values greater than 13.47.

This equation represents a transformation of the parent function y=x^{6}. Firstly, the coefficient −1000000000 induces an extreme vertical stretch, causing the graph to narrow significantly and undergo a reflection across the y-axis due to the negative sign. Secondly, the term (x−6.2)^6 results in a horizontal translation of 6.2 units to the right, effectively shifting the graph horizontally. Additionally, the constant term 10.35 leads to a vertical translation, raising the entire graph by 10.35 units along the y-axis. Furthermore, the inequality 7.75<y<10.35 restricts the range of the function, confining the y values to lie between 7.75 and 10.35. Overall, these transformations combine to produce a vertically stretched, horizontally shifted, and vertically translated version of the original sixth-degree polynomial function, within the specified range.

This specific equation represents a transformation of the parent function y=x^7. Firstly, the coefficient 9999999 induces an extremely large vertical stretch, significantly elongating the graph. Secondly, the term (x−8.65) ^7 leads to a horizontal translation of 8.65 units to the right, effectively shifting the graph horizontally. Additionally, the constant term 5.8 results in a vertical translation, lifting the entire graph by 5.8 units along the y-axis. Furthermore, the inequality 5.7<y<6.2 restricts the range of the function, confining the y values between 5.7 and 6.2. Overall, these transformations combine to produce a vertically stretched, horizontally shifted, and vertically translated version of the original seventh-degree polynomial function, within the specified range.

This equation represents a transformation of the parent function y=x^3. Firstly, the term (2.95x−26) ^3 leads to horizontal compression and translation. The compression occurs due to the coefficient 2.95, which narrows the graph horizontally, and the translation of 26 units to the right shifts the graph horizontally along the x-axis. Secondly, the constant term 5.6 results in a vertical translation, raising the entire graph by 5.6 units along the y-axis. Furthermore, the inequality 5.5<y<6.4 restricts the range of the function, ensuring that the y values lie between 5.5 and 6.4. Overall, these transformations combine to produce a horizontally compressed and horizontally shifted version of the original cubic function y=x ^3, with the range restricted to values between 5.5 & 6.4.

The equation represents a transformation of the parent function y= sqrt x. Firstly, the term sqrt 1.425x−16.75 introduces a horizontal compression and translation. The compression occurs due to the coefficient 1.425, which narrows the graph horizontally. Additionally, the translation of 16.75 units to the right shifts the graph horizontally along the x-axis. Secondly, the constant term 5.8 results in a vertical translation, raising the entire graph by 5.8 units along the y-axis. Furthermore, the inequality 11<x<12.75 imposes a restriction on the domain of the function, ensuring that the x values lie between 11 and 12.75. Overall, these transformations combine to produce a horizontally compressed and horizontally shifted version of the original square root function y= sqrt x, with the domain restricted to values between 11 and 12.75.

The equation represents a transformation of the parent function y=8^{x}. Firstly, the term -0.3^(x−5.25) introduces a horizontal compression and reflection. The compression occurs due to the coefficient −0.3, which compresses the graph horizontally, and the negative sign reflects the graph over the x-axis. Secondly, the constant term 7.05 results in a vertical translation, raising the entire graph by 7.05 units along the y-axis. Furthermore, the inequality 5.3<x<6.488 imposes a restriction on the domain of the function, ensuring that the x values lie between 5.3 and 6.488. Overall, these transformations combine to produce a horizontally compressed, reflected, and vertically shifted version of the original exponential function y=8 ^x, with the domain restricted to values between 5.3 and 6.488.

This equation represents a transformation of the parent function y=\frac {1} {100x}. Firstly, the term y=l\frac {1} {-40\left(x-12.5\right)} introduces a horizontal translation and compression. The expression −40(x−12.5) compresses the graph horizontally, while the translation of 12.5 units to the right shifts the graph along the x-axis. Secondly, the constant term 14.5 results in a vertical translation, lifting the entire graph by 14.5 units along the y-axis. Additionally, the inequalities 11.5<x<13.5 restrict the domain to values between 11.5 and 13.5, while the inequalities 13<y<16 restrict the range to values between 13 and 16. Furthermore, the parameter l, which ranges from 1 to 4, acts as a slider that scales the amplitude of the function, effectively stretching or compressing the graph vertically. Overall, these transformations combine to produce a horizontally shifted and compressed version of the original function y=\frac {1} {100x}, with the domain restricted to values between 11.5 and 13.5 and the range restricted to values between 13 and 16, while the slider l allows for adjustable amplitude scaling.

This equation represents a transformation of the parent function y=ab^{x}. Firstly, the term 2.2^(8.7x−83) introduces horizontal compression and translation. The base 2.2 compresses the graph horizontally, while the translation of 83 units to the right shifts the graph along the x-axis. Secondly, the constant term 5.35 results in a vertical translation, lifting the entire graph by 5.35 units along the y-axis. Furthermore, the inequality 8.6<x restricts the domain to values greater than 8.6, while the inequalities 5.25<y<5.55 restrict the range to values between 5.25 and 5.55. Overall, these transformations combine to produce a horizontally compressed and horizontally shifted version of the original exponential function. y=ab ^x, with the domain restricted to values greater than 8.6 and the range restricted to values between 5.25 and 5.55.

The function describes a transformation applied to a point in a two-dimensional space. The angle a indicates a rotation while the variable t represents time or maybe another parameter (I'm not exactly sure) with f(t) being a function of t. The transformed x-coordinate of the point is given by t cos a - f(t) sin a + 5.5. This expression combines a rotation by angle a with a horizontal transformation based on f(t) scaled by sin a and a translation of 5.5 units. Similarly, the transformed y-coordinate is given by t sin a + f(t) cos a + 9. This expression combines a rotation by angle a with a vertical transformation based on f(t) scaled by cos a and a translation by 8 units. Together, these components create a transformation that rotates, scales, and translates the original point in the plane. The specific nature of the transformation depends on the functions f(t) and the angle a.